SS Ambient Occlusion relies on the values written to the depth buffer.
As long as something is written to the depth buffer, it will be included in the effect.
This SSAO from depth setup is an all-or-nothing effect. So even semitransparent sprites cannot have "just a little ambient occlusion".
I think you want to slide the Depth Alpha Cutoff slider value higher so that more of the semitransparent things on your sprite do not get written onto the depth buffer. If the alpha is already at 0, I'm not sure at the moment why they are still included. I'll have to check how this shader writes depth. It's possible that it doesn't take vertex alpha into account.
Immediately though, note that even if you set the alpha to 0, the potential pixels are still being checked and calculated by the GPU (even if it's less calculation). This isn't specific to Spine.
So if you are hiding parts of your Sprite, it's better to disable/hide the parts altogether, instead of setting color alpha to 0. This way, their shapes will also not be written to the depth buffer.