In MTG: I attack with a 3/3 crt. and my opponent declares a 3/3 crt. as a blocker then I play.....?

Then I play a different creature's ability (which can be played as an instant would) killing my opponents 3/3 blocker BEFORE damage was dealt between the two 3/3 creatures. Is this correct?Also, does my 3/3 crt still get damage through to my opponent? Since I killed the blocker before damage was traded.