WordNet sense 1 (the bodily process of discharging waste matter):

evacuation, excretion, excreting, voiding

WordNet sense 2 (analysis of a problem into alternative possibilities followed by the systematic rejection of unacceptable alternatives):

reasoning by elimination

WordNet sense 3 (the act of removing or getting rid of something):

riddance

WordNet sense 4 (the murder of a competitor):

liquidation