Can I cut the wood between struts in my attic?
I am just going to confirm what has already been stated in the comments but add a little more to it. Yes the slats are to help keep spacing and are not structural.....anymore.

During the construction of the roof system these are also used to keep the trusses from falling over with the help of a number of diagonal braces before the plywood roof sheathing is put down. I have in the past, seen in the install guide for roof trusses how to place these braces during assembly, including the diagonals. There has never been a reference about removing them later, but I see no reason to leave them. 

As a mention, instead of cutting them out, bring a hammer with you or pry bar and remove the whole thing. Cutting them out brings to mind rough ends, possibly splinters a plenty, and if you are a big guy as I am, while moving between the trusses, the less things to rub against or snag onto the better.