We have to assume that you have 3 reliable handlers, capable of quickly moving the disc around the cup comfortably. If you don't at least have this, then I am afraid all hope is lost...

Firstly, remember that every time a defender takes something away, they are giving up something in return. For example, if your marker forces your forehand, he is taking away the backhand at the expense of giving up the forehand throw. If your defender marks up on your back shoulder, he is taking away the deep strike at the expense of giving up the in-cut.
The same principle is true in a zone situation. By playing a 3-3-1, the "cup" focuses on preventing upfield passes from the handler, at the expense of leaving the other handlers (usually) wide open. They want to prevent significant upfield movement, and for you to eventually turn the disc over by dropping a pass or trying some high-risk junky throw (and if you don't have skilled handlers, they will likely get their wish).
Take what the defense gives you. Be patient, dump-swing constantly, wear down the cup and pick your moments. The cup will get exhausted chasing the disc back and forth across the field, which opens space up for short gains. Dump quickly, swing quickly, and follow your passes for little fetches and give-and-go passes. By the time the cup catches up you've gained some yards. Repeat as necessary...and I can recall points where it's taken upwards of 60 or 70 passes in a row to get from one end of the field to another...oh, and if the cup is loose or inexperienced, throw some fakes and make them pay for it. Try breaking the mark from time to time, keep them honest.
Something for the cutters to focus on is properly engaging the mids - keep your feet moving and making cuts and force them to follow you. Have someone engage the deep defender by acutally going deep...that way he can't help out the mids. Overload one side so that the defender can't cover both of you: one cut to the disc, one cut away from the disc. Force the defender to make a choice between one or the other, and take what they give you. Stretch them out horizontally - if you attack the entire width of the field, they'll have to respond to that.
But above all, have your handlers practice, practice,
practice!