I wonder if you could capture that energy and use it to generate thrust.
Most of the energy is coming from your thrust so it'd be a lossy process however if you're able to capture all of the energy then there won't be anything left to damage the ship.
(I'm asking genuinely here. My analogy might be wrong because it's too classical!)
There are a few engineering difficulties with the idea but it makes for some good SF stories...
[1] The momentum vector just completely flattens almost any other physical characteristic. I'm not sure there's even enough time for nuclear fusion to take place.
But then there's e=mc^2, so if the stuff you're running into is the fuel source for your fusion engine (could be a fission engine, but unlikely you'll run into heavy atoms like Uranium or Plutonium) then you have an unlimited source of energy...
So maybe sort of? Running into things slows you down, but then you capture that mass and release the energy out of it to go faster... because of the nature of e=mc^2 you'll usually get more energy out of something if you convert its mass than what you lose by running into that mass.
The issue is that the energy for that explosion comes from the slowing down of your ship, so it doesn’t work.
For the same reason that the power of an atomic bomb does not depend on how fast you smash the sections together - it depends on how much mass is converted to energy in the resulting reaction.