How to disconnect from an administrative boundary?

A quick warning first: This forest area is tagged as landuse=forest, this can include forests managed for things like paper production where areas may be clear-cut and re-seeded. Recently cut or seeded areas are generally considered to still be part of this kind of landuse.

Assuming that's not the case here:

This forest and heath are mapped as part of multipolygons. These are relations used to describe more complex areas made up of several different ways. In this case the border line was used as one of the outer ways of the forest multipolygon so the forest doesn't have dedicated geometry here.

A good description of how multipolygons work is here on the wiki.

This is quite a large edit for one session in iD. You are probably better off using something like JOSM. JOSM can view a way this long without dropping out of edit mode and has a relation window that displays relations in a better format (closer to the way they are described and stored).

If you use iD:

The easiest way to correct the forest geometry is probably to:

• Add a node to the way shared by the heath and forest at the point where the forest breaks away from the existing line.
• Split the way at this point.
• If you now select the way to the left of the new split and scroll down on the left panel you will be able to delete the way from the forest relation (iD describes it a little backwards).
• You can also now delete the border way from the forest relation.
• Now draw a new way from the split you created to the other end of the border way following the edge of the forest
• Add the new way to the (correct) forest relation using the + symbol under the relations heading in the left panel.