Bisect means to divide into two equal parts, to cut in two. Bisect comes from the prefix bi- which means two, and the Latin word sect, derived from the word secare which means to cut.
Dissect means to cut apart methodically in order to learn about the internal workings of something, especially a dead animal or plant. Dissect is also used figuratively to mean to analyze something piece by piece. Dissect comes from the prefix dis- which means apart and the Latin word sect, derived from the word secare which means to cut.