Is Knoxville East of the Mississippi River?

No.

There are a small areas that are west of the Mississippi River. For example if you look at the area where the Missouri, Arkansas and Tennessee borders meet you can see a small area on the west bank of the river that is part of Tennessee. If you follow along the river you should be able to spot a few more.

There are several areas of TN that lie west of the Mississippi River , comprising 1000's of acres. The exist due to the river channel changing over the years , creating oxbow lakes.