The story
Alluding to Hamlet. The two senses result from two interpretations of the word coil, one taking it to mean “tumult, confusion, fuss”, the other “case, wrapping”. In either case, the phrase shuffle off this mortal coil must mean “die”. Since shuffle off in this case is generally taken to mean “get rid of” or “evade”, it is likely that in the sense that Shakespeare used it, it was specifically referring to the act of suicide.
Etymology from Wiktionary, CC BY-SA 4.0.