I never cut anything thinner than 1/4". So, If I need an 1/8" piece, I will stack another layer of 1/8" material. Trying to cut thinner material is difficult as you don't have proper control of the piece and tear out can occur.
Because I do two to four craft shows a year I always stack four layers of 1/8" BB plywood. I use a no. 1FD UR or a no. 3 FD UR blade with minimal tear out on the back which is easily sanded off.
Before you start, sand your blanks to Finish grit, usually 220 grit. Then make your stack and cut. Then use some 220 grit sandpaper to lightly sand off the fuzzies.