Which variety of Euphorbia do you have? There are quite a few!. I take it that this is outdoors and evergreen? It may be one of the sub-shrubby types such as E. characias in which case if you cut all stems back, you will lose the flowers on the one year old stems. Older stems that flowered last year of this species can be cut back if they haven't already started to die back.

Herbaceous types with dead stems above ground can of course be cut back soon, preferebly just before shoots emerge in spring.

If it's one of the succulent or semi-succulent shrubby species that are used indoors, they can be pruned to any point on the stem where they will send a new shoot out. Like all this group, be careful when cutting back any Euphorbia species as the milky sap is caustic.

Yes, watch out for the sap especially on a sunny day as this seems to trigger the reaction. Clean your secateurs afterwards too as they will be sticky. Most Euphorbias have biennial shoots. That is, they grow in year 1 and flower in year 2, then trim them out right to the base. Leave any that didn't flower as they will flower next year.