Mark the polygon, press e to get all the nodes and then press g to unglue them.
Utilsplugin2 has it Help/Action/SelectWayNodes – JOSM
When there are multiple polygons connected with each other in a street block, to avoid disconnecting them inside, search eg child (parent (child selected) highway=*) & (child selected)
Instead of ungluing, you can use Parallel, then Replace Geometry. If the latter fails, you can still unglue first, but it can still be replaced to the Parallel shape without needing to move yourself.
In addition to the replacement method mentioned above, you can use scripts for more complex edits in JOSM:
https://wiki.openstreetmap.org/wiki/User:DressyPear4/SepararPoligonosGrudados
Draw the correct boundary as an untagged way, then use Alt-X from the utils plugin linked above to cut the land use into two parts, then delete the wrong section
Search corrected to keep polygon (child (parent (child selected) highway=*) & (child selected) ) | selected