What is the origin of the saying "Heavens to Betsy" ?

No one knows for sure.

"The big Oxford English Dictionary has a first citation from 1914, but I'm told it can be found as far back as 1891. Some have tried to trace it to the Revolutionary War and to Betsy Ross, but have failed; others think it may have something to do with the frontiersman's rifle, often called Old Betsy, but there's no evidence that saying and name are associated. Charles Earle Funk, who in 1955 used the phrase as part of the title of a book about curious phrases, said that its origins were 'completely unsolvable'."

http://www.quinion.com/words/qa/qa-hea1.htm