Scrub like crazy with a push broom. As you can see in the photo, I'm preventing the mat from moving by standing on an edge.

Brush in a couple of different directions so you agitate all the contaminants from various angles.

No push broom (or other stiff brush) handy? No problem! Take your shoes and socks off, and scrub with your feet. Just be careful to not slip off the mat. You do not want to rub your feet up against concrete, or whatever surface the mat is on.

As a bonus, you will have the cleanest feet in the tri-state area after this procedure.