Thank you for reaching out.

You can try smothering it out by using a can or dark container to cover the stump to deprive it of the sunlight.  This method may take some time to do.

There are also methods where you drill into the stump and add a concentrated, systemic herbicide like glyphosate or triclopyr to the hole.  I’m not sure if it will affect the raspberries or not. Systemic means it travels throughout the tree. Triclopyr can leach into the soil, where glyphosate is unlikely to leach.  I’m no expert on chemicals so I am just passing on research and not something I have tried.

I’ve also read about applying salt or vinegar to the hole you’ve drilled, but I understand both kill the organisms in the soil and it doesn’t come back, so I’d advise against that method.

No matter what you do you may continue to get suckers trying to come up for some time.  This won’t be a one and done if you don’t get rid of everything.

Good luck.