I've been off tanking garuda lately and pretty much the green add does not need to be picked up at all since it should be up for 10s maximum with all the dps switching to it and blowing it up. Your role as the offtank is to pickup the red add which usually is able to be picked up with ease via using provoke-> tomahawk/shield lob until in range -> Enmity combo.

You can pickup both adds if you REALLY want to, although this is only possible if one add spawns next to you allowing you to put out an enmity combo then do the above on the other add.