Mounting a Used Diamond Blade
I'm going to cut to the quick on this one (pun totally intended). If you have a saw that you use to either run different sized diamond blades on, or you use specialized blades for each type of cutting you do, getting a used blade mounted correctly on your cutoff saw is important to the life of the blade. And mainly what I'm talking about is the orientation of the diamond grit in the blade.
Some blades have only a small indicator on the label as to which way the blade should be facing to make sure it spins in the intended direction. If the label gets damaged, there doesn't seem to be another way to tell which way the blade should be turning. But there is, and it's pretty simple. Just look at the diamond segments at the end of the blade.
What you see pictured below is a close up picture of a diamond segment on a cutoff saw blade. From the picture you can see that the diamond grit or bits kind of "leading the charge" when digging into the material being cut. The matrix material behind each piece of diamond is protected by that diamond bit, at least until that diamond fractures and falls out; then the matrix material will soon follow, getting quickly ground away by the material being cut.
So think of it like a comet - the head of the comet is going in the direction you should be cutting. Mount the blade accordingly. Do this and you'll help get the most out of your blade.