A 75-cm diam chopping secondary mirror has been developed for the 15-m diam James Clerk Maxwell telescope. The large focal ratio (D/F = 1:0.36) requires a highly convex secondary mirror, which was manufactured out of a solid slab of high-grade aluminum, consisting of a 3-mm thick shell with a support ring along the edge. The mirror surface approaches a predescribed hyperboloid with a rms precision better than 9 microm, which is adequate for use in the submillimeter wavelength region. The design aspects, the performance of a two-axis chopping mechanism, and the construction of the mirror are described.