Hello Chris,
You can go to Tennessee Property Data Home Page which is a public site and type in certain subdivisions or street names to find properties that have sold in the last 9 months but I know of no way to find homes that have no morgages. You can also go to the Bradley County Courthouse and look up information for properties that have sold .

Theoretically, you could go to the courthouse and look at recorded deeds, then cross reference that with recorded liens. In practice it would be very difficult and time consuming to do so.

CRS (Courthouse Retrieval System, the program that Realtors use to search tax records) has certain searchable fields, whether or not a property has a mortgage is not one of those fields unfortunately.

The information is available as part of the public record but I'm not aware of any program that will let you easily search for it.