If I understand correctly, for your bit, I agree that you need to make 3 passes to get the correct width. Each pass with your bit can widen the slot the bit's width (at most), which is 12 mm. Set the bit depth to 12.5 mm (but if the shank is less than 12.5mm, you should use another bit, for safety). I'm assuming that you either have a straight edge to run the router along, or an edge guide, or your table has a fence. The 3 passes might be something like:
Pass 1: Let this be the left-most pass. You now have a slot 12 mm wide at the base (the bit width).
Pass 2: Move your straight edge (or guide or fence) over 10 mm to the right. This is the middle pass. You now have a slot that's 22 mm wide at the base.
Pass 3: Move over 9 mm to the right. This is the right pass. After this pass, you now have a slot that's your desired 31 mm wide.
For pass 3, you might want to creep up on the overall width, by moving say, only over 7 or 8 mm and checking the overall width of the slot.