When you want to select and delete a wire *segment* in Circuitmaker you'll notice that it instead selects the whole wire. Bummer, no? No! Not if you know how to use Break Wire. Here's the tip:
1) Right click the wire in question
2) Select Break Wire from the context menu that pops up
3) Hover over the wire and notice that the wire segment has a little "breaky" thing on it.
Now pro users will know that if you cycle the Space bar while you have the little selection element hovering over the wire, that it will cycle between a small break, a medium break, and the whole segment. See image(s).