It sounds like you want to express a situation where tapping on the stone will turn it into a horse gradually, step-by-step, each tap making the stone slightly more horse-like, until with the 100th tap (or the final one), the metamorphosis will be complete.
It also sounds to me like you want to know if the progressive verb tense, e.g.: tapp-ing, will convey that meaning. (Please clarify if that is not part of your question, and I will get rid of the first part of my answer.)
First of all the example in your question really doesn't have a progressive tense verb in it. "Tapping" is actually a so-called "gerund", and acts as a noun in the sentence.
But either way:
"Tapping on the stone [100 times] turns it into a horse."
or (with present progressive tense)
"When one is tapping on the stone [100 times], it turns into a horse."
The "-ing" suffix on tapping doesn't carry that kind of step-by-step "progressive" implication by itself. Using a couple of examples that are a little easier to imagine:
"While they were dancing they fell in love."
"When he was doing his evening yoga exercise, he figured out the
The "-ing" in "dancing" and "doing" doesn't imply that falling in love or figuring out the answer took place gradually or progressively. Those effects might have been sudden (-- or not, but the "-ing" doesn't give you that information.)
So if you want to describe a gradual, progressive, step-by-step effect, an adverb (progressively ?), or maybe a whole multi-word description will be needed to get the point across.
This example (stone into horse) is so specific, unusual, and outside my usual experience, it's hard for me to grasp whether "progressively" is the right adverb for that meaning or not. Maybe "incrementally" might be closer.
I think if you really want to get that full meaning across, (especially the part about 100-taps for a complete transformation), you might need to describe it in finer detail than just one adverb, ... like maybe a whole sentence.