The shutter was a mirror. At the time did they have a shutter behind the mirror, or use the mirror as the shutter?
Wikipedia's article on the history of SLR camera
Early 35 mm SLR cameras had similar functionality to larger models, with a waist-level ground-glass viewfinder and a mirror which remained in the taking position—blacking out the viewfinder—after an exposure, returning when the film was wound on. Innovations which transformed the SLR were the pentaprism eye-level viewfinder and the instant-return mirror—the mirror flipped briefly up during exposure, immediately returning to the viewfinding position.
Now, when the viewfinder blacks out, that means that the mirror has been raised to take a picture. If the mirror did not return instantly, or even worse, did not return until the film was rewound, this would mean that the shutter would be the only thing keeping the film from being overexposed. To solve this problem You could add a film door, and use a leaf shutter, but this complicates matters.
Mirrors are heavy. Shutters are light enough to be moved in small fractions of a second.
In a twin lens reflex camera, the mirror reflects the light entering the viewfinder lens, to the viewfinder screen at the top of the camera. The mirror doesn't need to move. because there's another lens below for the film.