It doesn't look particularly healthy to me. Did deer eat it or did somebody prune it with dull pruners or loppers?
These euonymus are somewhat prone to insect attacks, mostly from scale and aphids; I actually see it quite often. Euonymus has its own species of offending scale. Hopefully its health hasn't been compromised by them, they can transmit diseases.
Theoretically, yes you can prune it down to thicker parts and have it flush again with new growth.