Yes, it is both persistent and invasive. The best way to manage IMO is old fashioned hand pulling methods augmented by a hand digging tool. It is critical when digging that you remove ALL of the plant including all of the roots...all of it, 100%. Otherwise, you aren't really getting anywhere. Be sure to remove each plant in its entirety from the garden space...i.e., don't just throw it on the ground in your garden space or compost pile or it will return with a vengeance.
Sugar is one organic control that works...but for me hand methods are just the best.
Once you get control it is critical that you never leave your soil barren and open to re-infestation. Cover crops really help with that...in fact are the only way I know to do long term prevention.
I'd bet that nutgrass is the number one reason or close to it a lot of people give up on gardening after starting out. Getting it under control and keeping it under control makes for a Happy Gardener.