Euphorbia millii (crown of thorns)only reproduce (asexually) by cutting and (sexually) by seed
... they dont have offsets, it sounds like a confused growth... i get that sometimes on my euphorbs, its a prostrate growth split between trying to become an inflorescence (flower
cluster) and a new branch... you may see tiny mutated and undeveloped flowers
and leaves randomly mixed together... this occurs in a mix up of hormones, dont worry, ive always seen it as a good sign: a happy plant
and just got confused...im only guessing, but a picture would be best... hope this helps!!!!