When the water is that laden with crud, you should pre-filter the water with something like a coffee filter to remove as much of the algae and particulates as you can, just so they won't overwhelm and instantly clog the Sawyer mini. The filter is capable of removing any bacteria or cysts that are in that water, which is your main health concern. The taste will not be great, but it ought to be safe.

Definitely use some of your filtered water to thoroughly backflush the mini filter afterward. A clogged filter won't do you any good.