An atom is normally electrically neutral .Why then should an alpha particle be deflected by the atom under any circumstances?

Answer 1

What if the alpha particle, which has a + charge, gets near the nucleus of the target atom? Then it is inside the electron shell of the target and feels mainly the repulsion force of the positively charged nucleus. Remember Gauss's law that it is only the charges inside (at a lower radius than) the shell you are at that cause an electric field where you are. That is for uniformly charged shells of course, but that is the idea.

Answer 2

and remember also that an atom is mostly empty space, so the nucleus is a powerful repulsive force.