I'm not familiar with Globe Amaranth (Gomphrena 'Pink Zazzle') but it sure is a pretty plant and I'd either pinch back the dead flower heads or as green stated, use pruners to cut just above the next set of leaves below the dead flower head.
edited to add: Welcome to ATP Cherie!
~ I'm an old gal who still loves playing in the dirt!
~ Playing in the dirt is my therapy ... and I'm in therapy a lot!
