tmux maintains its own copy buffer; when mouse support is turned on, highlighted text will be saved there rather than the system clipboard. However, it’s relatively easy to access this data.
# Output current save buffer to STDOUT.
#
tmux save-buffer -
# Push tmux save buffer to system clipboard on Linux.
#
tmux save-buffer - | xclip -selection clipboard
# Push tmux save buffer to system clipboard on macOS.
#
tmux save-buffer - | pbcopy