Oops, with due respect to the poster, there is mass transit at night. That is, it is true the MRT shuts down, however both SBS and SMRT buses run skeletal services from city area to the suburbs from say midnight to about 5AM. Note that these services are rather limited so one has to take into account the possibility of taking a cab.

Noting the OP's question was targeted towards airport services after midnight, in that specific case there really is no mass transit available during the wee hours of the night, however this is not true with regards to Singapore overall.