A toilet flushing assembly includes at least a spiral trapway and a drive mechanism. The spiral trapway includes an upstream portion coupled to a toilet bowl, a curved portion, and a downstream portion coupled to a waste outlet. The drive mechanism is coupled to the spiral trapway and configured to rotate the spiral trapway from a first orientation to a second orientation. The first orientation evacuates contents from the toilet bowl and the second orientation advances the contents from the spiral trapway to the waste outlet.