By using several mirrors, the light path can be contained into a smaller area. This means that different color light will be focused differently when passed through the lense, resulting in a blurred image. This is called chromatic abberation. Mirrors do not have this problem. Mirrors are very efficient and do not absorb light.
Lenses are heavy and can only be supported around edges.
If they get too big, they warp and distort the image. Mirrors can be supported over entire back surface and can be made out of lighter plastics. A mirror only needs one precision surface. A lense has 2. Lenses are formed by pouring molten glass into a mold and then polishing.