Tmux mouse-mode on does not allow to select text with mouse

If you press Shift while doing things with the mouse, that overrides the mouse protocol and lets you select/paste. It's documented in the xterm manual for instance, and most terminal emulators copy that behavior.

Notes for OS X: In iTerm, use Option instead of Shift.  In Terminal.app, use Fn.

Thomas Dickey's answer is probably what most people are looking for.

To give some more context on the behavior you are observing, when tmux's mouse mode is on it enables text selection within a particular pane. That's the red text highlighting shown in your screenshot. It can be useful when you have split panes and want to only copy text within one.

When you release the mouse button the selected text is copied to tmux's internal clipboard. You can then paste that text using Ctrl+B ].

Unfortunately it does not copy to the system's primary clipboard, so you can't select in tmux and then paste into a browser for instance. You can configure that behavior though. See this answer to How to copy and paste with a mouse with tmux.

I had a similar issue where mouse click and drag (tmux-yank) stopped working on MacOS, try Cmd+R