Unfortunately, unlike Phil Mickelson, most of us won't be able to take a perfect divot that can easily be replaced. Most of us would dig up a good portion of turf and damage the green.
So before you try something similar, ask yourself - if you're not a highly skilled player - if it's really worth the potential damage to the green.
But, according the Rules of Golf, there are no prohibitions on the type of club to be used on putting surfaces.

