The mirror being up likely refers to the viewfinder mirror. I haven't used a DSLR, only mirrorless, but I wonder if that could be independent of the shutter.
That's exactly the mirror that gives (D)SLR's the R ("reflex") in their name. It's in the path between sensor and lens and redirects the image towards the view finder. When taking a picture this mirror moves out of the way and the image is projected on the film/sensor instead. The advantage of that system is/was that the photographer can preview the image as it will get captured.
