Looks to be a blue spruce (picea pungens). Like all spruce, if you cut it leaving no buds, the branch is dead even though it may be two years until all the needles fall off. The best routine, IMHO, is to wait until after the season's new foliage has hardened (roughly sometime after the summer solstice) AND you can see buds at the bases of some needles. Then you can cut back to a bud. I haven't a clue where you are, but I've preferred to do this in August. This will induce back budding, even on the trunk of a reasonably healthy tree.
The rest is water, lots of sun, and lots of nitrogen (which is best to apply after the summer solstice until temperatures are dropping below 40F).
You will find many published recommendation to pinch new growth. IMHO, this is, at best, a refinement technique and is useful only for limiting the length of new shoots. Done improperly, you get a new shoot with nothing but a set of terminal buds (nothing to cut back to).