Do mud tires waer faster?

No

The wear rate of tires is based on the rubber compound used when making the tire. Softer rubber generally gives better traction because it grabs the road surface better but it will wear out faster. Harder rubber will last longer but won't "grab" the road quite as well.

Mud tires are simply tires with deep tread and wide groves designed to sink into soft road surfaces and give lots of space for mud & water to flow away from the tire. A mud tire with this tread pattern could be made from a soft rubber that might only get 30-40k miles of on-pavement driving or can be made from a harder rubber that might last 60k miles or more.

Yes, they do. .