The invention discloses a tooth cutting method for a bevel gear with spherical involute toothed archimedes spiral teeth and a machine tool thereof. The method overcomes the disadvantages that the current tooth cutting method forms principle errors, has complex revision calculation, trial cutting and adjustment of a machine tool, and the like. The tooth cutting method adopts a machine tool with double stations and a single cutter head, which can continuously tooth dividing. When teeth are cut, the I station at one side of the cutter head completes the rough cutting of tooth sockets and the finishing cutting of the concave tooth surfaces of teeth; then the II station at the other side of the cutter head completes the finishing cutting of the convex tooth surfaces of the teeth, each cutter tooth straight edge on a cutting tooth cutter head envelopes and cuts out the side surfaces of the teeth, the circular arc edge of tooth top cuts out the tooth root, and the rough cutting concave edge cuts off the margins of the tooth sockets; and when the teeth are cut, a cutter head shaft and the tooth blank shaft are in a spatial cross position, the rotating end surface of the cutter head is perpendicular to the tangent plane of the gear blank base cone, the cutter head, the gear blank and the big circular plane of an imaginary spherical surface rotate in an uniform speed, the cutter head is in the rotary feed when cutting the teeth, and the continuous hobbling base cone toothed portion is the spiral bevel gear of Archimedes. The invention provides a machine tool, a cutter head and a cutter tooth for realizing the tooth cutting method.