If I put the Stunning Blow feat on the Arkhman Asylum Ventriloquist figure, would his Incap SP do two damage instead of one?

Please quote the powers in question please.

I would assume so, but my buddy doesn't think so. What do you think?

They are both replacement values so they would not stack. You would replace once to 1 with his special power then again using stunning blow. So no they would not stack.

Always include the actual wording of the mechanic in question to get the most accurate answers:
So what you end up with with is two effects that deal 1 damage. So normally, this would deal a total of two damage. But in the case of attacking a character with toughness, for example, you'd deal 1 damaged, reduced to 0, and another 1 damaged, reduced to 0, for a total of 0 damage.

Actually, Stunning Blow is not a replacement value; it actually doesn't affect the character's damage value at all. It just causes the character to deal damage equal to its unmodified damage value.