Mass transport through graphene is receiving increasing attention due to the potential for molecular sieving. Experimental studies are mostly limited to the translocation of protons, ions, and water molecules, and results for larger molecules through graphene are rare. Here, we perform controlled radical polymerization with surface-anchored self-assembled initiator monolayer in a monomer solution with single-layer graphene separating the initiator from the monomer. We demonstrate that neutral monomers are able to pass through the graphene (via native defects) and increase the graphene defects ratio (Raman I_D/I_G) from ca. 0.09 to 0.22. The translocations of anionic and cationic monomers through graphene are significantly slower due to chemical interactions of monomers with the graphene defects. Interestingly, if micropatterned initiator-monolayers are used, the translocations of anionic monomers apparently cut the graphene sheet into congruent microscopic structures. The varied interactions between monomers and graphene defects are further investigated by quantum molecular dynamics simulations.