Diamond saws are designed to be the most durable blades for the most difficult saw projects. You will not need to worry about damaging the diamond saw blade itself. These blades are made to withstand stone materials. The soft fibers of wood boards will not hurt the blade itself. The danger is in how the diamond blade treats the wood itself.
General purpose dry diamond saw blades can be used for several materials, but reconsider before using them to cut wood. The harsh grit of the diamond blade can cut tile and masonry with straight lines. When applied to wood, however, the blades might create a rough cut, ripping apart fibers, or might make it too easy to create crooked cuts. In most cases, it is better to use a traditional steel blade for wood.
Carbide-tipped saw blades are designed especially for wood. These are similar to diamond saw blades, but are designed with teeth and coatings that will make it easier to cut wood, especially hardwoods. If you do want to use a diamond saw blade, ensure that you use a carbide version that is specifically designed for wood.
Some exceptions exist to using diamond blades on boards. For example, fiber cement board comes in planks and might resemble wood, but it is actually made from cementitious materials. Do not assume that the board shape means it is made of wood. Diamond saws work well when cutting fiber cement and similar materials for construction products.