While this operation is completely possible, when you see the "Test Execution Details" tab, you'll encounter the warning that the "Tests" field is not available:
That warning is a field lock that we added because when there are to many associated Tests, editing the field will cause screen blockages and system failures due to response times.
However it will not prevent you from being able to clone the issue, it just doesn't allow you to either add or remove any links.
You will always have that same option in the view screen to be able to add or remove Tests.