Could you please put the meat from the grill on your plate while I change the grill?
Do you mind taking your meat off the grill for a minute so I can give you a clean grill?
この場合、次のような言い方ができますよ。
ーCould you please put the meat from the grill on your plate while I change the grill?
「グリルの網を替える間、お肉をお皿に取ってもらえますか?」
to put the meat from the grill on your plate で「お肉を網から取ってお皿に置く」
ーDo you mind taking your meat off the grill for a minute so I can give you a clean grill?
「きれいな網に交換するのでちょっと肉を網から取ってもらえますか?」
to take your meat off the grill で「網から肉を取る」
ご参考まで!