The invention discloses a pull broaching or push broaching device for non-linear surface grooves and surface grooves different in width. The device comprises a plurality of broach cutter heads, an inner cutter bar or an outer positioning cover, a clamp and a pushing block. The broach cutter heads can be combined to form a broach; cutter teeth are arranged on each broach cutter head; guide pillarsare arranged in the inner holes or outer circumferences of the broach cutter heads; each broach cutter head can rotate around the inner cutter bar or the outer positioning cover; guide slots are formed in the inner cutter bar or the outer positioning cover; the guide slots are consistent to processed non-linear slots in shape; the guide pillars on each broach cutter head are embedded into the guide slots. Therefore, during machining, each broach cutter head moves along the tracks of the guide slots to process the non-linear slots; when the broach cutter heads move toward different track slotson two sides separately to further process the surface grooves different in width. The device disclosed by the invention expands the range of pull broaching and push broaching processing greatly and enriches machining processes.