I control an Elvish Aberration enchanted with Burning Anger. My opponent plays a Constricting Sliver and chooses to exile my Aberration. Am I able to tap my Aberration to deal 4 damage to it before my creature gets exiled?
Assuming you have controlled Elvish Aberration continuously since your most recent turn began, you can activate the ability Burning Anger grants to Elvish Aberration in response to the ability Constricting Sliver grants to itself (C.R. 117.7, 117.1a, 302.6). An activated ability (such as the former) or a triggered ability (such as the latter) has no effect unless and until it resolves (C.R. 608.2c, 609.1, 602.1, 603.1). In this scenario, if Elvish Aberration leaves the battlefield before the latter ability resolves, it will be an illegal target for that ability (C.R. 608.2b).
Also note, that removing the sliver before its triggered ability resolves will make it not exile the targeted creature, because the duration of the exile ended before it began.
See also this thread.
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