In Inkscape we can break apart the path at a desired location.

1. Ungroup all paths from the source SVG  
2. Select nodes from where we wish to break the path  

   ![enter image description here][1]

3. Tick *Break Path at selected nodes* ![enter image description here][2]  
4. Choose *Path > Break apart* <kbd>Shift</kbd>+<kbd>Ctrl</kbd>+<kbd>K</kbd>  
5. Select the now generated new object to then change it's color (or delete it, move it, etc.)  

   ![enter image description here][3]

In case there are no pre-existing nodes at the location we need to break we can always manually add new ones.

  [1]: https://i.sstatic.net/OcdGc.png
  [2]: https://i.sstatic.net/wB8Af.png
  [3]: https://i.sstatic.net/FN1Gv.png