I want to remove the picture not to replace it with another.
This was asked two years ago, I had forgotten about this one. The new version of Skype has an option to remove/hide profile picture:
Still haven't found relevant information on removing it using the web version.
Best Answer
Easiest solution would be to replace the image with a generic picture, like the Skype logo or a blank user avatar picture.
As far as I know, you cannot remove a profile image once one is added as it is stored on Skype's servers. The other option would be to create a new account.