I can't find any reliable source proving Sarah Butcher as this Anne's mother or even as a wife of Samuel Waddy. The only link I find for her is on a Family Search listing that has her listed as Sarah Butcher Owen, daughter of Thomas Owen and her mother being a Brookes, so Butcher not even being her maiden name. There's no documentation, it's just from gedcom uploads:
https://www.familysearch.org/tree/person/details/GQM4-BHW
Some Ancesstry trees show this Anne's mother as Ann Craighill, so I searched for info on her and found much more:
http://www.carolshouse.com/familyhistory/waddy/
https://www.genealogy.com/forum/surnames/topics/waddy/238/
http://www.familycentral.net/index/family.cfm?ref1=5885:4551&re...
https://www.genealogy.com/forum/surnames/topics/waddy/329/
https://thepreterite.wordpress.com/2012/02/20/turner-waddy-c/
Even when Samuel's wife's maiden name isn't given, she is listed as Ann, never as Sarah and he and Ann did have a daughter named Ann.
So unless someone can better document Sarah Butcher Owen as the mother of this Anne (Waddy) Tate, I propose her mother be corrected to Ann Craighill.