Cutting Polygons in QGIS at a specific distance from a feature in another layer

You will need to buffer the selected line (path) at the distance you require and then cut those out of the other polygon using difference.

If it was an operation you needed to do very often then it would be worth writing a python script to carry out both operations together.

In this workflow you will need refFunctions plugin, to use geomintersects().

  1. Open attribute table of your Polygon layer.
  2. Activate Field Calculator.
  3. Tick on Update existing field and select <geometry>from the pull-down menu.
  4. Provide this expression: difference($geometry, buffer(geom_from_wkt(geomintersects( 'Your_LineLayerName', '$geometry')), 20))

Please modify Your_LineLayerName which is your (path) layer, and 20 (buffer size) as required.

NB. Since the change is made instantly and irreversible, please be careful and keep a copy of your original Polygon file.