Mechanical exfoliation techniques are widely used to create high quality graphene samples for analytical use. Increasingly, mechanical methods are used to create large quantities of graphene, yet there is surprisingly little molecular insight into the mechanisms involved. We study the exfoliation of graphene with sticky tape using molecular dynamics. This is made possible by using a recently developed molecular dynamics forcefield, GraFF, to represent graphene's dispersion interactions. For nano-sized flakes we observe two different mechanisms depending on the polymer-adhesive used. A peeling mechanism which mixes shearing and normal mode exfoliation promotes synthesis of graphene rather than many-layered graphite. Armed with this new chemical insight we discuss the experimental methods that could preferentially produce graphene by mechanical exfoliation. We also introduce a mathematical model describing the repeated exfoliation of graphite.