Take it however you like to explain it - and unfair it may seem - but it is covered in the FAQs. A mulligan will cost you 2 strokes - even if it is a putt.
So in the normal game - a putt does not degrade your ball meter.
But in a practice game - a putt will cost you 2 hits on your ball meter.
A mulligan is a stroke that is replayed from the spot of the previous stroke without penalty.
Mulligans can only be used in Practice mode as a single player playing on a stroke play course.
If you use a mulligan during a Practice game, the ball you are using will be degraded by two hits instead of one hit. Mulligan putts will also degrade your ball by two hits.
No, there is no limit on the number of mulligans you can use when playing a Practice game.