How to clean a very textured patio with deep mud and rust stains?
OK, you've got two problems: rust and deep mud. I would bet the deep mud is mildew.

First the rust stains. Pour some white vinegar on the rust stains and let it soak in for 10 to 20 minutes. Then scrub with a hard bristled brush, then rinse with cold water.
For the deep mud, mildew, you're going to need a power washer. You can buy or rent one at your home stores. Get one that's about 2000 PSI. In most cases, plain water is all you'll need. If not, get a stone prewash. Good luck