Simpson was born in San Antonio, Texas, to Curtis T. Simpson and Joyce Alice Adams. He married Tina Drew on August 19, 1978, when he was 20 and when she was 18. They had two daughters, Jessica and Ashlee.
In a GQ magazine interview, he said about his daughter Jessica: "Jessica never tries to be sexy. She just is sexy. If you put her in a T-shirt or you put her in a bustier, she's sexy in both. She's got double D's! You can't cover those suckers up!"
He formerly was a Baptist minister at the Heights Baptist Church in Richardson, Texas.
The song "(Antichrist Television Blues)" on Arcade Fire's 2007 album Neon Bible is reportedly about Joe Simpson, though bandmembers have not confirmed that association.