Let's pack up the leftovers and take them with us.
Tips
usage
Standard phrase counter staff use to ask 'for here or to go?' in fast food and bubble tea shops. Compare 堂食 ('eat in') for the opposite. 打包 alone can mean 'to pack' more broadly (including software packaging); the 带走 makes the takeout meaning explicit.
culture
After a restaurant meal, asking the waiter to 打包 leftovers is normal and not at all impolite - China has a strong anti-food-waste culture (光盘行动, 'clean plate campaign'), and packaging up extras is encouraged.