If you are finding that doing an on-demand Time Machine backup from your mac is terribly slow, follow these steps to speed up these backups.
Please note this should only be a temporary process, as it will affect the performance and battery life of your Mac.
To do this - Open Terminal and type the following command:
sudo sysctl debug.lowpri_throttle_enabled=0
And that's it. Now if you stop your Time Machine Backup and start another one, you'll notice the transfer speeds considerably improved.
Once you have finished doing your on-demand Time Machine Backup, make sure to revert the change made by going back into Terminal and typing the following command:
sudo sysctl debug.lowpri_throttle_enabled=1