The rotors are the key components in the Roots pump, and the rotor manufacture time will decide the pump price. In special cases, such as when one rotor shaft has two stages, respectively, with claw-type and Roots profiles, the traditional forming method is unsuitable for manufacturing the Roots rotor stage. Instead, more suitable manufacturing methods, such as planning or end-mill milling, can be applied. However, these two methods take time and effort. Therefore, this study proposes a general mathematical approach for Roots rotor manufacturing using the conical milling cutter as the key tool, which can reduce manufacturing time. The contact points and meshing angles between the rotor and the conical milling cutter can be calculated based on contact conditions. Then, a 3D conical milling cutter surface is obtained based on the cutter profile as a straight line, and the conical cutter is designed and considered to avoid undercutting in the rotor cutting process. The generated Roots rotor can be obtained by applying cutting simulation from the proposed mathematical model. The normal deviations of the rotor can be found by comparing the generated rotor profile to the datum rotor profile. In addition, the influence of axis errors of the conical milling cutter on the tooth profiles of the Roots pump rotor is investigated and discussed. The experimental results based on the proposed mathematical model are obtained and expressed to confirm the practicability of the proposed method.