Gilmartin, 25, appeared in 50 games during his rookie season, going 3-2 with a 2.67 ERA and striking out 54 batters in 57 1/3 innings. He was acquired from the Twins in the Rule 5 Draft in December.
Goeddel, 26, faced four batters in the ninth inning of the Mets' 13-7 win over the Dodgers in Game 3 of the Division Series and didn't get any of them out. One of the four hits he gave up was a three-run homer by Howie Kendrick.
Matt Reynolds, who replaced shortstop Ruben Tejada on the roster after Tejada was injured in Game 2 of the NLDS, stays on the roster.