Great-Grandma Sawyer is the deceased mother of Grandpa Sawyer.
She is first mentioned in The Texas Chainsaw Massacre 2, where Drayton Sawyer proudly states, "O Great-Grandma in Chainsaw Heaven!" Her preserved body is kept in the Texas Battleland Park's attic. Stretch took the mini chainsaw from Great-Grandma Sawyer's hands, and used it to slay Chop-Top.
It is possible that she had an incestuous relationship with Grandpa.
It is revealed by Tobe Hooper on the commentary DVD, that she is in fact a great-grandmother.