Certified GKH Gardening Expert
I only see mention of cutting them back in the fall. Some articles say they don't need staking, others say they do.
You might sacrifice blooms if you cut them back before flowering and interrupt the bloom cycle. You can try dividing your plant in spring. Then cut back one plant and leave the other and see how the cut one performs.
https://www.gardeningknowhow.com/ornamental/bulbs/anemone/japanese-anemone-care.htm
https://plants.ces.ncsu.edu/plants/eriocapitella-x-hybrida/
http://www.missouribotanicalgarden.org/PlantFinder/PlantFinderDetails.aspx?kempercode=h310