Hello, I use a MacBook Pro (Retina, 13-inch,Early 2015), doing double backups on two Maxtor external drives at regular(ish) intervals with Time Machine.
I had the same problem after updating to Mojave about 10 days ago. Now, having just further updated the system to Mojave 10.14.4, I tried backing up again, but again the backup got stuck and would not complete.
In the meantime I remembered having problems with excessively slow backups some years ago, and getting around that by temporarily (just for the time of the backup) disabling my security software (in my case Sophos version 2.1.0). Eventually the matter got fixed and I did not need to do that anymore. However, in this case I thought I'd try the same strategy again: perhaps, as before, there was some incompatibility between the update and the security software, so temporarily disabling the latter may allow me to do a complete backup. Well it seemed to work!
I've just completed my first post-Mojave backup on one of my two usual drives. It took a bit over one hour (not surprising as it was a big, ‘system update’ backup), but it progressed steadily and finished in the normal manner without getting stuck. Apple and / or Sophos (and other security software brands?) perhaps need to be aware of this in order to fix the matter. In the meantime I hope this tip may be of use to someone.
BTW I do not think temporarily disabling the security software puts one at risk, provided nothing 'risky' is being done during the security suspension spell. If anyone knows differently, I'd be interested to know.
Regards, Bea