If you damage a normal cactus' growth center(apex) it will start branching. The same way you get stem cuttings from most columnar cacti. I think the same should apply to euphorbias. Now I do say normal cacti- by that I mean the bulk of the species and genera are either columnar, or columnar-epiphytic(hylocereus), or short columnar(echinopsis). Id wait a while(a few months) and start these as cuttings, seeing as the original stem will never recover and decline slowly. Id say either frost bite or very severe sunburn...
We even had a thread/discussion where some members use a drill to "core" several types of barrel cacti to produce pups. The outcome is pretty much similar to yours.
