The idea of say, blasting the Earth with a 'Big Gun' (This can be any form of impact of course) to accelerate it sufficiently to reach an escape velocity from the Solar gravitational field is extremely unlikely. It would be possible I reckon, to wobble the planet, slow or speed up its angular rotation etc. maybe even push its orbit slightly to somewhat more or less parabolic or a slightly more and definitely can reach slightly smaller orbital radius.
HOWEVER, the energy required to acutally overcome the escaspe velocity from the sun, would be so large that the it would far sooner destroy the structural integrity of the mantle first, then potentially the (already superheated) core which would be (more) free to vent through the ruptured surface and likely rip the planet apart.