Is it possible to destroy proton in proton-proton collision?
Most proton-proton collisions will be elastic: throw in two protons and two protons will come out, deflected at some angle. But the more interesting collisions are those where individual constituents of the proton (quarks, antiquarks, or gluons) interact. For instance, all the interesting high-energy proton-proton collisions at the LHC are really collisions of two quarks, or two gluons, or a gluon and a quark (or similar combinations involving antiquarks) coming from the two protons. The results of this "hard" collision often come out at a large angle away from the proton beam, while the "remnants" of the proton that weren't directly involved in the collision sail off down the beamline in roughly the same direction the proton was originally going. It's probably reasonable to say that the original proton was "destroyed" in this process, although some large fraction of its energy and its constituents keep moving in the same direction.
Of course, the word "destroyed" is a little fuzzy. The protons don't just disappear. There are a few constraints on the final result of the collision process: it must conserve momentum, energy, and baryon number. A proton has baryon number +1, as does a neutron and various heavier "hyperons," whereas an antiproton has baryon number -1. The momentum, energy, and baryon number can all be divided up in complicated ways. So you might argue that there's a sense in which you didn't "destroy" the protons, since at the end you still have to have a total of 2 baryons. But in general, the proton remnants moving down the beamline could join up with antiquarks and make mesons with no net baryon number, while baryons could form from the hard collision and move away at a large angle. In that case I wouldn't say there's any sense in which the original protons maintained their "identity," and I think it would be reasonable to say they were destroyed.
All things considered, though, it's probably best to not think in terms of the word "destroy" that you chose at all. Maybe the way to visualize it is like this: most proton-proton collisions are like two billiard balls that bounce off each other in an elastic way. But the collisions that are of the most interest at a collider are more like cases where two billiard balls hit each other and small pieces of each shear off and fly out at a big angle, but the bulk of each ball keeps moving in roughly the direction it started from.
If changing the protons into something else counts as "destroying" it, then yes, this is what keeps stars burning.
In particular, two protons can interact and form a deuteron, a positron and an antineutrino and some energy.
The way you used baryon made me wonder if you are unaware of the baryon nearly conservation law.
From the link:
The baryon number is nearly conserved in all the interactions of the Standard Model. 'Conserved' means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. An exception is the chiral anomaly. However, sphalerons are not all that common. Electroweak sphalerons can only change the baryon number by 3.