Your Rosemary must be very healthy! Since he regularly takes clippings he could also use them to start a new plant by simply planting in a moist medium and water well. I find that during this time of the year Rosemary cuttings via softwood have some problems striking roots. Fall and spring is the ideal time for fast rooting.

I very much doubt that you can damage your healthy plant. Aside from clipping for use, I will severely prune my specimen several times a year. However, I do keep them in the peak of health.

If you wanted the total removal of a single bush, you could also dig the whole plant up. Yes, it will be shocked, but should survive, provided its well cared for. Mine here, will not survive a winter. As mentioned, a fall digging might be a better way to go for reducing transplant shock

Rosemary is easy to strike from cuttings, though it's slow to take off, and very slow to grow in its first year or so. The best cuttings are 'heel' cuttings.

Here is a link that might be useful: heel cuttings

^^^Thank you so much for your quick responses !

After my rosemary stalking neighbor left today I made a dash for the board here for some h-e-l-p !!

I may very well just give him a plant of his own !
He will never be patient enough for a slow grower and
if I do take out one of mine they are so large he probobly will kill it and goodness knows I can not wait till the Fall to do so anyway .

He is really quite generous in his own way and has given my plot the nod as a plant "rescue garden" . He has brought me near death hydrangeas, azaleas, bromaliads, and more that the studios would otherwise throw away after a premier or luncheon etc... I have thought about giving him a shopping list next time he heads out for work !!

I've started rosemary cuttings by clipping off about 6 inches, stripping off the lower leaves, dipping in rooting hormone powder, and then planting the cuttings in pots with either vermiculite or half potting soil/half vermiculite for drainage. They seem to do better in the spring, but rosemary is easy to start from cuttings, and roots very quickly, in my experience.