Does reinstalling a fresh Windows 10 on partition C remove viruses from other partitions, e.g. D & E, of my hard drive?
No. It would do exactly what you've stated, clearing out the C partition and reimplementing a fresh version of Windows.
It would likely remove any existing viruses affecting your current installation of Windows, but any infected files from your other partitions could still reinfect your new, clean installation, should you use them again.