WEAVE is the new wide field multi-object and integral field survey facility for the prime focus of the 4.2 m William Herschel Telescope. It is located at the Observatorio Roque de los Muchachos, in La Palma, Canary Islands, Spain. WEAVE fiber-fed spectrograph offers two resolutions, R 5000 and 20,000. It has a collimator mirror and two cameras optimized for the wavelength intervals of 366 - 959 nm and 579 - 959 nm, respectively. One of the responsibilities of INAOE within the WEAVE collaboration is the polishing of the collimator mirror, made of OHARA CLEARCERAM®- Z HS. The collimator has a diameter of 660 mm, a central thickness of 44.7 mm and a weight of 56.8 kg. The main specifications are: 2 fringes irregularity in a clear aperture of 624 mm diameter and a radius of curvature of 1224.65 mm +/- 0.15. In this work, we present the polishing process and final results for the collimator. In particular, we describe the tools developed for its manufacturing, the modifications carried out to the conventional polishing machine to support the glass. Additionally, the interferometric optical irregularity measurements are presented. The collimator polishing process is finished fulfilling all the optical specifications.