Using graphene-covered-microfiber (GCM) as a saturable absorber, the generation and evolution of multiple operation states are proposed and demonstrated in passively mode-locked thulium-doped fiber laser. The microfiber was fabricated using the flame brushing method to an interaction length of～1.2 cm with a waist diameter of～10 μm. Graphene layers were grown on copper foils by chemical vapor deposition and transferred onto the polydimethylsiloxane (PDMS) to form a PDMS/graphene film, which allowed light-graphene interaction via evanescent field. With the increase of the pump power from 1.25 W to 2.15 W, five different lasing regimes, including continuous-wave, conventional soliton mode-locking, multi-soliton mode-locking, a period of transition, and noise-like mode-locking, were achieved in a fiber ring cavity. To the best of our knowledge, it is the first report of the generation and evolution of multiple operation states by covering graphene on the microfiber in the 2-μm region. The results demonstrate that GCM can be a promising method for fabricating all fiber SA, and the switchable operation states can provide more portability in complex application domain.