Understanding the underlying mechanism in the tearing and peeling processes of graphene is crucial for the further hierarchical design of origami-like folding and kirigami-like cutting of graphene. However, the complex effects among bending moduli, adhesion, interlayer interaction, and local crystal structure during origami-like folding and kirigami-like cutting remain unclear, resulting in challenges to the practical applications of existing theoretical and experimental findings as well as to potential manipulations of graphene in metamaterials and nanodevices. Toward this end, classical molecular dynamics (MD) simulations are performed with synergetic theoretical analysis to explore the tearing and peeling of self-folded graphene from a substrate driven by external force and by thermal activation. It is found that the elastic energy localized at the small folding ridge plays a significant role in the crack trajectory. Due to the extremely small bending modulus of monolayer graphene, its taper angle when pulled by an external force follows a scaling law distinct from that in case of bilayer graphene. With the increase in the initial width of the folding ridge, the self-folded graphene, motivated by thermal fluctuations, can be self-assembled by spontaneous self-tearing and peeling from a substrate. Simultaneously, the scaling law between the taper angle and adhesive energy is independent of the motivations for thermal activation-induced self-assembly and external force tearing, providing effective insights into the underlying physics for graphene-based origami-like folding and kirigami-like cutting.