Should I Stop Stopwatch at the end of the method?

No, there is no need to stop or clean it up.

Stopwatch does not use any unmanaged resources (if you thought of IDisposable). It actually does not use any resources at all (except the memory used by the object itself, of course)! It also does not consume any CPU while measuring the elapsed time!

In windows implementations of .NET (full .NET Framework, Mono, .NET Core), it just calls the QueryPerformanceCounter() Windows API when needed (on Start() and Stop() and when reading Elapsed) to retrieve a high resolution time stamp.

In Linux implementations of Mono and .NET Core, it uses clock_gettime function to retrieve a monotonic increasing time value.

To anyone with a real curiosity about the implementation details: read this post.

I think Stop is useful if you want to reuse the Elapsed value.

No, you don't need to stop it. Stop() just stops tracking elapsed time. It does not free up any resources.