but generally I don't think you can just boot a backup of your system on another device, maybe from the sd card, but if the laptop is not an arm laptop it wouldn't work at all, and writing the backup to a usb would do nothing even for your pi possibly unless you had the right boot setup on the usb
A Raspberry PI ubuntu mate version is designated only for ARM processors, the SD card that the RPi uses as disk with / mount point doesn't have the boot flag that your laptop need to see for booting from it. Even if you set up this flag, it will not boot.
If you are trying to boot UM from USB on your RPi, you can read a bit more in this topic :