No Major League Met has ever thrown a no-hitter, but pitchers wearing Mets uniforms have thrown them in the minors and in spring training. I’m quite sure this list isn’t anywhere near complete, but I’m posting what I have to prove it can be done at some level. (additions/corrections welcome):

AAA

• May 29, 2001 - Steve Trachsel, demoted to AAA after a bad 2001 start with the Mets, throws a seven-inning, complete-game no-hitter for the Norfolk Tides. The Tides beat the Ottawa Lynx 3-0 in the opener of an International League doubleheader.
• May 15, 1992 - David Telgheder pitches a nine-inning no-hitter for the Tidewater Tides during a 1-0 win over the Pawtucket Red Sox. Telgheder struck out seven and walked three.
• 1988 - The Tidewater Tides’ John Mitchell throws a seven-inning perfect game (unsure of the exact date).

AA

• July 23, 2006 - Binghamton Mets pitcher Miguel Pinango throws a seven-inning no-hitter in the second game of a doubleheader against Portland. The Mets beat the Sea Dogs 7-0. (This has been cited as the team’s fifth its history but I can only find specifics on two more.)
• Aug. 2, 2003 - Binghamton Mets righthander Bob Keppel throws a 3-0 no-hitter against the Portland Sea Dogs, striking out one and walking three.
• Sept. 12, 1994 - Binghamton Mets pitcher Bill Pulsipher tosess a no-hitter during an Eastern League playoff game against the Harrisburg Senators. The Mets win 2-0.

A

• June 23, 2003 - Ken Chenard (5 in) and Mike Cox (2 in) combined for a seven-inning no-hitter during the second game of a doubleheader against the Brevard County Manatees. The Mets won 5-0 and the team notched its third no-hitter of the season.
• May 28, 2003 - Tyler Yates (5 in) and Chad Elliott (2 in) combine for a seven-inning no-hitter in the first game of a doubleheader against the Palm beach Cardinals. The Mets win 4-0.
• May 9, 2003 - Wayne Ough (7 in) and Mike Cox (2 in) combine for a nine-inning no-hitter against the Tampa. The Mets beat the Yanks 5-0 as Ough struck out eight.
• June 10, 1996 - Southpaw Joe Atwater throws a no-hitter for the St. Lucie Mets during the second game a doubleheader.
• June 29, 1995 - St. Lucie Mets lefthander Rafael Rogue strikes out 12 while tossing a no-hitter against the Dunedin Blue Jays during a 6-1 victory. The lone run scored on a walk and two errors.

Spring training

• March 21,1965 - Gary Kroll and Gordy Richardson combined for a nine-inning no-hitter during a 6-0 spring training game in St. Petersburg. Glenn in Troy notes a picture on page 30 of the 1965 Mets yearbook of Richardson throwing a pitch in the ninth inning and another of Kroll and Richardson getting congratulations from the Mets front office brass the following day.