The mesquite bows I've made were sapling bows: kids bows made from small diameter limbs with mostly sapwood. Mesquite is very stiff (when fully dry) and works well for powerful short draw bows. The wood is brittle in dry weather, however, so it might be best to back the bow with sinew...although the bows I have are not backed.
The wood steam bends easily, which is great for us who like to make double curve bows. Mesquite holds its shape very well if you steam and shape it when it's green. I haven't tried shaping Mesquite when dry, so I can't say how well it holds it's shape when heat alone is used.
The heartwood is different from the sapwood, in both color and strength. I think an all-heartwood bow will be stronger than an all-sapwood bow but it is hard to find a straight section of Mesquite (with a large enough diameter) for a bow longer than 40" or so. Also, sometimes there are voids in the heartwood that only show up after split and carve the wood...which can be very disappointing. There are also lots of knots in Mesquite, so you will have to spend a lot of time looking for that "perfect" stave.
I recommend harvesting only green Mesquite wood. Dead, standing Mesquite seems to be very brittle in most cases. And do not store the harvested Mesquite with the bark on! Beetles will get to it and the sapwood will look like swiss cheese in a few months (in warm weather). The heartwood is somewhat more resistant to the beetles but not much. I ALWAYS remove the bark and carve the wood down to bow dimensions before I let it dry out. I've had problems with checking but I also didn't seal the wood...so you might try shellac or something. Always seal the ends in any case.
(BTW - Thanks Cowboy)
