I think what your vet means is that he will take the biopsy whilst your dog is under for the teeth cleaning........That specimen will be put in formalin. You do not have to send it to the Lab until you want to. The specimen is not "clean". It is just on hold, until you send it.
It is something often done with animals, For example say a lump next the eye. It get removed, because it is unsightly and worries owner, lump is gone. Specimen is put in the fridge. lump comes back. Lump in fridge is sent for investigation to the lab.
This is often done, because owners do not want (or cannot afford) to spend money on labs and it might not be necessary.
If it was one of mine, I would send it straight to the laboratory to see what it was. So I could put it out of my head, I always worry about lumps and bumps.