GoWaterfalling is the premier source for information about Michigan’s many waterfalls. Their Slate River Falls entry says:
Slate River Falls is, unsurprisingly, on the Slate River. This is the largest of many drops over a three mile stretch of the river. This is a wild waterfall, with no fences, and the only trail is one left behind by the curious feet of others.
The falls are located along Skanee Road between L’Anse and Skanee, about 10 miles east of L’Anse. There is a sign marking the Slate River, so the falls are easier to find than some. The bridge over the river is just past Arvon Road. A few hundred feet east of the bridge there is a two track that leads to a small turn around. A rough trail starts here that follows the east side of the creek.
…If you continue upstream past the falls a few hundred yards you can find two smaller falls, Slide Falls and Ecstasy Falls (so named by kayakers). About 3 miles upstream you can find Quartzite Falls, Black Slate Falls and more unnamed drops. These falls can be reached by car. From Skanee Road head south on Avron Road, which is just west of the Slate River, for about 3.3 miles. Take the road to the right, which will soon cross the Slate River. A well groomed trail will lead you downstream to Quartzite Falls. Black Slate Falls and other drops are upstream and you just have to make your way along the river.