I asked about this a little while ago and got some good advice. I eventually took it all down to 10 inches or so and it's coming back great, really bushy. Here is a link that might be useful: Pruning Cotinus

Deadheading will absolutely help more blooms form. Don't know about when to move it. they are not native to the US.

welcome to the forums dave.. if you are going to hang around.. add your location on your member's page ... and if you dont think that is important.. i cant really tell you when its going to resprout .... e.g compare sara's z9 to my z5MI .... anyway ... i am pretty sure you could run this over with a cement truck and not kill it.. so stop worrying about that ... and with no insult to the root mass ... i would expect it to be back to the size you cut down.. in a year or 3... depending on location ... you might want to think about removal.. next time it tries to take over the yard ...unlike children.. you dont have to keep problem plants ... lol... unfortunately.. i dont remember if they bloom on new or old wood.. someone else will have to tell us if it will bloom this year .... so.. at worse.. you lose this years bloom ... ken

It looks a bit stressed to me. It is relatively newly planted and so might need more water. Actually stick your finger down into the soil a bit to see if it is lightly moist. If not it needs more water. The lawn care company is likely spreading an herbicide designed to kill broad-leafed weeds since I see no weeds, and that might be effecting it. At the least contact the lawn maintenance company to ask and enlarge the circle of mulch to decrease water competition and possible problems from lawn treatments. My preference as far as design is to include shrubs as part of a bed of plants rather than isolated in the lawn, so consider moving it. For suggestions of where, a photo of the yard would be needed. As others have mentioned, this isn’t a huge problem as far as this year’s foliage, but you want it well hydrated going into winter and you want to know what was causing the stress so that it can be remedied next season.