No. If you control Soul-Scar Mage (among one or more you control) and damage meeting its criteria would be dealt, it isn't; rather, that many -1/-1 counters are put on the creature in question instead (C.R. 614.6). Since the creature is not being dealt damage anymore, the effect of any other Soul-Scar Mage you control won't apply to that event (C.R. 614.7). This is so because replacement effects apply one after the other (C.R. 616.1, 616.1a-e).
EDIT: Edited after comment 3 was posted.
EDIT (May 23; Apr. 3, 2018): Clarification.
EDIT (Jul. 16): Correctness edit to conform to terminology change in Amonkhet.
Does having multiple Soul-Scar Mages in play under your control allow its effect to stack?
eg. 1 Lightning bolt = 6 x -1/-1 counters.
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EDIT: Edited after comment 3 was posted.
EDIT (May 23; Apr. 3, 2018): Clarification.
EDIT (Jul. 16): Correctness edit to conform to terminology change in Amonkhet.
No. Soul-Scar Mage's ability creates a replacement effect. Unless the rules for those change drastically before release:
The key point is that the mage replaces damage with something that's not damage, so it can't "accumulate."
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