There are several places where the state indicates it will not accept photocopies of ID, but I'm not aware of anyplace where they prohibit making a copy. Making copies of identification is a common, albeit unnecessary, practice in banks.
All banks are required to do for CIP purposes is keep a "description" of the identification they received. While a photocopy would certainly suffice for a description, so would "Tennessee drivers license, Exp XX/XX/XXXX, number XXXXXXXXX."
There is a much touted prohibition against photocopying military ID. In reality, it was intended only to provide leverage against people who were creating fraudulent military ID. However, military personnel oftentimes believe the "prohibition" is the gospel and get excited when a bank wants to make a copy. Accordingly, it's better just to write down the description.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.