The Observatoire de Paris is constructing a prototype Small-Sized Telescope (SST) for the Cherenkov Telescope Array (CTA), named SST-GATE, based on the dual-mirror Schwarzschild-Couder optical design. Considering the mirrors size and its specific curvature and the optical requirements for the Cherenkov imaging telescope, a non-conventional process has been used for designing and manufacturing the mirrors of the SST-GATE prototype. Based on machining, polishing and coating of aluminium bulk samples, this process has been validated by simulation and tests that will be detailed in this paper after a discussion on the Schwarzschild-Couder optical design which so far has never been used to design ground based telescopes. Even if the SST-GATE is a prototype for small size telescopes of the CTA array, the primary mirror of the telescope is 4 meters diameter, and it has to be segmented. Due to the dual-mirror configuration, the alignment is a complex task that needs a well defined and precise process that will be discussed in this paper.