In announcing the first award with Alec Baldwin, Mullally asked him to "give it to her" in what was meant to be a jokey sexual tone that viewers felt was cringeworthy.
One person on Twitter described it as "very bizarre sexual back and forth", while another suggested it was "ridiculous".
The SAGs celebrate a 25th anniversary today, with some of Hollywood's biggest names vying for a gong.
Bradley Cooper and Lady Gaga-led A Star Is Born is the top film nominee at this year's event.
Cooper and Gaga, along with actors Chadwick Boseman from Black Panther and Constance Wu from Crazy Rich Asians are among the presenters.
Australia's Margot Robbie has lost out to Emily Blunt in the category for Outstanding Performance by a Female Actor in a Supporting Role.
Legendary actor Alan Alda of M*A*S*H fame will be given the SAG Life Achievement Award by Tom Hanks.
Jodie Foster will present the evening's final award, for best motion picture ensemble, in a nod to the ceremony's first year. Foster won best film actor for Nell at the first SAG Awards.