Read rule 13.7 again: it says that attacked boxes AND minefeild hexes are eliminated if you advance into them (first hex of advance); for multi-hex advances only boxes can be eliminated that way, as you cannot do a multi-hex advance adjacent to a mine hex anyway: Multi-Hex AAC rule, second bullet, page 19.

As for normal movement, there is no rule allowing you to move over and destroy boxes or mines.