Each time you perform a copy (as in copy/paste) within tmux using its built-in
copy functionality (i.e. set-buffer and save-buffer), the text that you
copied to the buffer is recorded in the server's history.
Note: you may have Cmd-c or the mouse configured to copy to a tmux buffer.
So, while tmux paste-buffer (or Cmd-v if you have that configured) will
only paste in the most recently copied value to a tmux buffer, you can still
access more of the history.
Run tmux choose-buffer (or <prefix>:choose-buffer) to open an interactive
prompt that lists the tmux buffer history in reverse chronological order (most
recent to oldest).
You can navigate up and down through these buffers until you find the one that
contains what you're looking for. Then hit Enter and the value will be pasted
to the current window and pane.
See man tmux and search for choose-buffer for more details.