I'm not certain but are you having break out or is the plywood outer layer tearing away from the inner layers. If so, that is referred to as delamination. The most common cause is cheap plywood. The better grades of plywood you get from the big box stores are very poor quality and will delaminate as well as have voids between layers. I'm limited as far as a wood source in my area and usually have to resort to the box store quality. One way I've attempted to overcome the delamination is by double stacking with the two pieces I'm cutting facing each other. That will help but not eliminate the issue. Also, some patterns require you always place the pattern on the front of the piece of wood. Examples of this would be words in the pattern or certain things that require left and right orientation. If you double stack face to face, one of the pieces would be mirror imaged.
As Paul (Scrappile) said, quality wood is hard to find, especially Baltic Birch. If you do find it, the cost usually precludes the purchase. Another alternative would be milling down solid material but that can be very time consuming, and if you don't have the proper equipment, very expensive.
I also try to keep sharp blades in the saw. Again, it doesn't eliminate the problem but reduces the chance of serious delamination.