We appear to be looking at the non-drive side in the pic - and a normal tapered square-drive cartridge type? If so . . .
A solution I've used successfully is to use the crank bolt to bolt the removal tool to the axle (obviously on the drive side) - and as tight as you can get it into the splines (hopefully there are some bits left to grip!). You may need a couple of washers and depending on the removal tool a different one (this works with the Park Tool remover) - then with a big spanner try turning the tool to unscrew the cartridge. I hesitate to say it but I assume you are aware that the drive side is a LH thread . . . .
It also often helps, if you can, to loosen the non-drive side supporting cup as that sometimes grips the BB unit.
When you have the cartridge out, if the non-drive cup is plastic a bit of heat and some prodding with a screwdriver usually distorts the plastic enough to get it out.