I would not try to divide tuber at this stage. You can take cuttings to start another plant. It looks like you have a good shoot to do that. If you don't want to do that leave the strongest shoot and break off the rest. If you grow more than 1 the plants are weaker. One tuber has to divide it's energy to support all those plants thus giving inferior flowers.

I planted Dahlia Tropical last month and notice last week that there is a new shoot. I wasn't sure if I should just leave it or cut it.

I did notice that the stem of my Tropical is a lot thinner than my pom pons. Is that typical?