Unless the spell or trap is continuous, no. Mystical Space Typhoon's text is pretty specific, as it says only, 'destroy', not 'negate and destroy.' Now, since every rule has its exceptions, continuous spell cards like Yami and Umi, which stay on the field, are destroyed by Mystical Space Typhoon, their effect ends, but only by them being sent to the graveyard. So Mystical Space Typhoon can not be used to counter an opponent's spells.