Assuming that you can't fix this without removing and replacing the subfloor (I can't think of anyway to "do it right" without doing so but I'm not all knowing in that area). To cut out the subfloor, you can use your circular saw for all but the corners. Since you know the thickness of the floor, just set your blade such that it's depth is exactly the same thickness (or slightly less) than the floor and have at it. If you aren't cutting beyond the depth of the floorboard, then there is no chance to cut into a joist. At the very least, this will allow you to cut a larger hole so that you can better evaluate what's under it.
For the corners and/or next to the wall, I recommend investing in a oscillating tool. And a straight cut blade (ones on the left):
You don't need a nice oscillating tool for this small job and a cheap one can be had (at least in the US) for $20 from Harbor Freight or similar store (+$5 to $10 for the blade).
When it comes to how to patch it after it's removed, that entirely depends upon what's underneath that you have to work with. Since this is under a toilet (and you plan on tiling when its all said and done), it needs to be rock solid. You might have to expose more than your 1'x2' area to make it work and you will likely need to end up with something similar to this:
-edit- here is the video the above image came from that shows cutting out and replacing subflooring due to water damage by a window.
Considering you have plumbing you will have to work around, it might not be an obvious or simple fix and you may have to update the question (or ask a new one) after you get the subfloor removed.