Like many Southwesterners, I frequently use mesquite to smoke flavor meats. The trick is not to use too much.
Since mesquite is such an assertive wood, I definitely would not mix it with another.
When I use mesquite, I prefer to use it on its own. For a brisket, I'd use 1 4x4x2 inch piece or 2 2x2x2 inch pieces.
As you can probably tell from earlier posts, it's very easy to overdo mesquite, but it has a unique flavor that blends well with beef.