The vote did not occur. In the middle of the debate Sen. Bob Corker (R-TN) moved to table (kill) the amendment, forcing an immediate vote. The Senate then voted to kill Paul's amendment, by a vote of 61-36.
The post-9/11 AUMF has been interpreted broadly by US presidents as allowing unlimited war-making powers against anything even loosely described as "terror." Sen. Paul argued that the AUMF was wrongly been used to authorize seven distinct wars, and that repealing it would force Congress to debate specific authorizations for specific wars as an alternative.
While he'd hoped this would bring in support not only from opponents of the war, but from hawks eager to get their votes on the record to authorize these many, effectively unauthorized wars, little support ultimately materialized. In addition to Sen. Paul, speaking in favor during the debate were Sens. Ben Cardin (D-MD), Chris Murphy (D-CT), and Dick Durban (D-IL).