The option to ask other sims to break up comes from The Sims 4 Get Together expansion pack. It is located under the Mean interactions (because you are mean to the sim you want that sim to break up with). This can be done by any sim, but if the relationship is low, it won't work.
Here's what you should click to find this interaction: Mean.../Other Sims.../Ask to Break Up with...
If the sim is on the same lot, you'll see them break up immediately after the action is complete. If not, you'll recieve a text message later saying that sims have broken up.
This is actually part of influencing NPCs' relationship feature. The interactions are located under Other Sims... category: Talking other sims up and hooking sims up are part of friendly category while asking sims to break up and trash talking are located under mean category. Additionally, you can ask other sims about other sims to find out the relationship between them.
Or have I accidentally stumbled in The Sims 3 discussion?