David Weaver
saw the kerfs part of the way, remove the waste with a chisel until you're just short of the saw groove and then saw the rest of the way.

I'm not aware of any saw that will clear sawdust well that deep without being extremely coarse (like a toolbox saw with giant induction hardened teeth), and those tear up the work.

sawing half depth and then full depth once the lateral waste is removed allows the saw teeth to clear dust.