Methods for forming cutting elements, methods for forming polycrystalline compacts, and related polycrystalline compacts are disclosed. Grains of a hard material are subjected to a high-pressure, high-temperature process to form a polycrystalline compact. Inclusion of at least one relatively quick spike in system pressure or temperature during an otherwise plateaued temperature or pressure stage accommodates formation of inter-granular bonds between the grains. The brevity of the peak stage may avoid undesirable grain growth. Embodiments of the methods may also include at least one of oscillating at least one system condition (e.g., pressure, temperature) and subjecting the grains to ultrasonic or mechanical vibrations. A resulting polycrystalline compact may include a high density of inter-granularly bonded hard material with a minimized amount of catalyst material, and may provide improved thermal stability, wear resistance, toughness, and behavior during use of a cutting element incorporating the polycrystalline compact.