Every time we flush our toilet it backs up out of the gas eacape vent. My question is how do I clean up the fecal matter?

You are going to have to bite the bullet and get this fixed. Cleaning it up will only fix it until next time but anyway my advice, a large shopvac.

Use either a shovel or a doggie poop scooper. It is not as hard as physics...

Or a tiller or shovel and turn it under, but you have to get the drain cleaned out so it stops happening.

everytime we flush our toilet it backs up out of the gas eacape vent. My question is how do I clean up the fecal matter?

I assume that you're on a septic tank that's loaded up and needs pumping. Also get your drain field checked to be sure it's operating correctly.
As for the spill in your yard, shovel up what you can and spread lime over what's left. Good luck, Tom