Remember 'Growth follows the Knife.'
The honeysuckle is doing its best to replace what you cut off. Watershoots, more usually referred to on fruit trees are rapidly growing non-flaowering shoots.
You can tip them, but do not cut back so brutally and you will have lots of flowers next year.
Honeysuckle in hedges get trimmed every year, but not too radically, and they flower every year.