As in, it forces the star to undergo rapid nova/supernova by contracting the star. It then redirects the force of the nova/supernova out the back end, via ricocheting the force around the ship till it exits the ship out the back end.
Problem needing to be solved: surviving the nova/supernova
How does it survive?
As Randall Munroe once wrote: "what would be more bright: A megaton nuclear bomb detonated against your eye, or a star going supernova as far away as the earth is from the sun?" The answer was the supernova. It is simply a ridiculous thing, releasing more energy than any rational person can understand. To put it in another way. Iirc the quote was in the answer at what point you could be killed by neutrinos. These are famous for practically not interacting with matter. You can fire them through the Earth and measure them (with great difficulty) on the other side with barely a hitch, as they don't really interact.
A supernova creates enough neutrinos that if all the other insane violence was ignored, these things that basically do not interact with anything will still kill you.
To give some other ways to put it into perspective. It is more energy than our sun outputs in ten billion years. It is estimated that an Earth like planet would need to be 50 lightyears away to not feel damaging effects. If the sun would go supernova, our planet is estimated to get to 15 times the temperature of the sun's normal surface temperature.
There is no material that can withstand the shock, heat, anything of the EM spectrum, the sheer energy of microscopic particles and even the neutrinos.
Your main problem is dealing with the extreme radiation. Like Cadence said in their comment, however big you think supernovas are, they're bigger than that.
Hard EM. Hard everything. Hell, even hard neutrino radiation.
Assuming you have some magic material that can deal with all of that though... (Perhaps a domain wall, which in some models are stable and 100% reflective.)
Asymmetric supernovas eject material unequally in different directions, and may even propel their stellar remnants (neutron stars) at high velocities away from the blast. A hypothetical "supernova starship" can make use of that by artificially inducing asymmetry during core collapse, when small influences propagate into large ones, creating a "shaped supernova blast". You can point the explosion vector away from the ship to make this craziness slightly easier to handle from an astro-engineering perspective, or you can direct it into whatever lines your reaction chamber to exchange more momentum.
If you really do have a perfect reflector, which you'd damn well need as anything less is briskly annihilated, a better option might be to contain the blast (or two) and open a hole whenever you need a little thrust.
It would need to be
$$\huge \text{ BIG}$$
Huge I mean.
Like enormously. Mind-bogglingly. Big.
So big that in fact. That you quite can't wrap your head around it.
We have loads of questions around here about big things. Some of the big things are as big as a planet or even as big as a star. But a supernova is even bigger than a star. And the upshot of the existing questions is that even the marginally big things in the existing questions are already too big to not collapse under their own gravitational pressure, from excessive and flagrant bigness.
So I say give up on realistic physics. Just wave your magic wand and say it works because I said so. And start worrying about how the heck you use a supernova as a power source anyway. A supernova only lasts a moment. You get loads of power all of a sudden and then nothing.
If you want to use a normal star instead of a supernova, feel free to look up Stellar engines for inspiration. The nerds over at Orion's Arm have already written extensive fanfiction on the subject.
The glowy thing in the middle is a star by the way.
It survives with copious amounts of Handwavium, with a liberal sprinkling of Sci-Fi super-material with borderline magical properties.
E.g Super-duper-Special-Reinforced-nano-Carbon-steel-polymer-molecular-crystalline-engineered-biogrown-Space-plate.
As I said in a comment: You would die from neutrino radiation (!) alone, and you can't shield against it.
Such a bold idea needs bold science: You'll have to slow down time, bend space, or generally change the fabric of spacetime, as I suggested in an answer to the question how to shield a planet from a supernova.
In all likelihood you'll need energy in the order of magnitude of the explosion in order to shield against it. Such energies are generally not available. The most elegant — indeed, probably the only — way would be to use the energy delivered by the explosion to establish the shield, very quickly and in an escalating fashion.
About as realistic as an answer can be, because as others have said, there is no surviving a supernova unless you are many light years away. Freeze time around the supernova when it's most compressed and grab a scoop small enough to fit in your ship. Once it's in place, resume time in extremely brief pulses, with a duty cycle such that the rate of energy released is sufficient to power a fusion engine.
Edit: Even if you did this, as @Jens said, it's still waaaay overkill. In the spirit of fueling ships with supernovae, you could take the same approach, but build a gigantic reactor around or near a time-frozen supernova. The reactor facility takes that unimaginable amount of energy and uses it in particle accelerators to generate copious quantities of anti-matter, or perhaps some far-future handwavium fuel, depending on how far down the rabbit worm hole you want to dive
We don't use hydrogen bombs to propel cars.
We won't use supernovae to propel starships. Not even in science fiction.
For basically the same reason: a major efficiency mismatch. The energy used to propel is the tiniest of a fraction of the energy released (1044 Joule, while 1027 J is enough to boil the Earth's oceans). Almost all of that energy is wasted and everything near the business end gets destroyed. Save a star today, use a garden variety anti-matter or warp drive.
Under physics as we know it? No.
The energy keeping the ship together would be less than the energy of the nova. And there is no way to make matter that can withstand that energy, because such material would, even if it did exist, require more than a super nova to shape.
Basic principle is this. If you are dealing with more energy than is needed to shape a material, then it is enough to ruin any shape you make. If you can hammer a metal into the shape of a ring, hitting it twice as hard will ruin the ring. And anything that can suirvive an explosion, would need more energy than that explosion to shape.
In addition to all the problems already pointed out you have the detail of acceleration. Let's suppose you have some handwavium shield between the detonation and the ship and the ship is strong enough to take it. Your crew isn't, we're talking thin red paste across any floor.
Maybe you could cheat. A lot.
Here's what you do. You figure out a way to create a stable wormhole where at least one end doesn't have to be fixed (YOU don't have to do this, you can just say the scientists in your story figured it out.)
You put the non-fixed end in your spaceship. (Oh, also you need to be able to anchor this wormhole end to a physical object. Good thing your fictional scientists are so good at sciencing.)
You put the other end near the star you're about to supernova.
When it goes, "stuff" (whatever that might be) from the supernova goes into the stellar end of the wormhole and comes out the ship end of the wormhole. Your fictional scientists may be semaphoring a bit here, because I've been saying "wormhole" but what you really want is a Portal from the game of the same name, where momentum is only SORT OF conserved ... the magnitude IS, the direction ISN'T.
This allows you to take a small (and hopefully survivable) portion of the supernova energy and use it for propulsion of your ship.
Of course, this is HORRIBLY wasteful. If it's cheap and easy to generate the portals then you could just keep resetting the stellar one a bit further out (and shifted slightly) so you get another slice of the pie instead of letting it go to waste.
Might be better just to drop the stellar end of the portal inside the star and NOT make it go supernova. Then you get starstuff coming out the other end at whatever pressure exists at that point. You could siphon off a LOT (in human terms) of starstuff without hurting the star noticeably, because A LOT (in human terms) is a rounding error on a rounding error in stellar terms.
