To blindside is to launch a surprise attack, especially one that comes from an obstructed or hidden place. Your video game army might blindside your friend's army, resulting in your victory.
If you come up from behind your brother and shove him, you can say that you blindside him. There is also a more figurative way to blindside someone — simply to do or say something the person is utterly unprepared for. You could blindside your family, for example, by suddenly announcing that you're moving to China. The oldest use of blindside as a verb, around 1968, referred to a football tackle.