Mate, use gnome-screenshot instead of mate-screenshot

I resolved the same issue by adding the --interactive option

gnome-screenshot --interactive

Actually, mate-screenshot does have the utility you want, (see man mate-screenshot) so there's no need to install an extra package. In a terminal, you can use the -a flag

mate-screenshot -a

This turns the pointer into a cross-hair and you can click and drag to select the area you want to grab.

You can set a custom shortcut for it (for example shift+prt sc like gnome-screenshot) in:

System > Preferences > Hardware > Keyboard Shortcuts

click the + Add button to add a custom one.

You may well find that using the command mate-screenshot -a in the keyboard shortcut does not work, in which case you need to modify the command to call bash and set DISPLAY... First check the variable in a terminal:

echo $DISPLAY

and take note of the output. For me it's :0.0

Then use this command in the shortcut setting:

bash -c "DISPLAY=:0.0 mate-screenshot -a"

Replacing :0.0 to match the output from echo $DISPLAY