Jagged and stonebound have hidden multipliers that get averaged between all parts of a tool when it is built (stonebound has a positive multiplier, jagged has a negative), so it's not accurate to say stonebound 'stacks.' Also, both jagged and stonebound work the exact same way. Ardite has a stonebound multiplier of 2.0, though, so it has a higher possible bonus (the other stonebound multipliers are 1.0 and cactus has a jagged multiplier of -1.0).
What this all boils down to is that the more stonebound/jagged pieces of a tool there are, the higher the multiplier will be of the final tool. But, if you only have one piece with stonebound in a tool made of 4 pieces, you're only going to get a quarter of that multiplier. The only way to get the 'full' bonus is to have all the pieces of the tool be the same material (whichever material has the highest multipliers; in this case, Ardite and Cactus).
I'm planning to make things like this more transparent in my TiC Tooltips
EDIT: Weird side note, if you make a cleaver using two cactus pieces and two non-ardite stonebound pieces, you'll end up with something that has both the 'Jagged' and 'Stonebound' abilities but neither will actually do anything (the multiplier will have averaged to 0.0).