Is it normal for a mole on the back to cause severe pain?

No, never. A benign mole should never cause severe pain. Please see a dermatologist asap to rule out an abnormal mole. I hope this information is helpful. Stephen weber, M.D., f.A.C.S. Lone tree facial plastic surgeon.
No. Moles never hurt unless they are traumatized, or become infected. In most such situations the pain is coming from something in the vicinity of the mole, but not the mole itself. Either way, if you are experiencing severe pain for any reason, you need to see your doctor and find out why.