My grandmother died of melanoma of the vulva and my mom had cancerous tissue removed from her breast, what are my chances of catching cancer?

Hard to tell. ...With the info available but i would suggest you talk to your family doc or gynecologist. They can perhaps refer you to a specialist in genetic cancer risk who will take a full family history and determine if you need genetic testing. He/she can also advise you of ways to reduce your cancer risk. Best to you and happy tg.