The hydrogen is bonded to an element in mineral acid which have tendency to pull electrons towards itself. So the other element say Cl in HCl pulls the electron of H making it behave like proton bonded to Cl-. When such a system come in contact of other atom like water that have tendency to pull positively charged particles (such as protons) towards it, the proton will detach and so the HCl molecule will break up into H+ and Cl-. In this way mineral acid dissociate to give proton.
Similarly H is bonded to O in H2SO4ā. Oxygen also pulls the electron from H and it dissociate into 2H+ and SO42- in water.