The 3-3-1 zone defense gets its name from a formation of 3 players up front, 3 in the middle, and one deep.
This is what it looks like with the disc in the middle of the field, forcing flick (for a right handed thrower). The 3 defenders up by the disc are commonly referred to as the "cup". Only one person in the cup can be within 10 feet and initiate the stall count. Each position has a specific role.
Number 1 is the designated "mark" who will guard which ever player ends up with the disc. After catching up to the disc, the mark is primarily responsible for taking away the around on the break side. This is throw you want to shut down.
Number 2 is the middle or "top" of the cup, and is primarily responsible for ensuring that the disc does not get thrown through the gap between them and the mark.
This is throw that number 2 tries to shut down. The mark can help with the I/O, but since the mark is the only one who can stop the around, they cannot fall for I/O fakes.
Number 3 is the last person in the cup or "chase", and their role depends on the force. If the disc is being forced to the side line for a trap, then the chase may take away the throw between them and number 2.
In that situation, this would be throw that number 3 must shut down. Again, number 2 can try and help with the I/0, but there primary role is the gap between them and the mark.
More commonly however, defenses will attempt to use a cup and force the handler to throw into the middle .
In that force mid situation, number 3 will take a slightly wider alignment and the middle middle AKA "mid-mid" or "small monster" will shut down the disc being thrown between 2 and 3. This is the throw they are hoping the offense will be tricked into making.
Free from the concern of the gap between themselves and number 2, number 3 can focus on ensuring that any disc movement to the force side is lateral and not down field.
This is the throw that number three wants to shut down.
It is important for number 3 not to get too wide from the top of the cup, otherwise the mid-mid will not be able to fill the gap.
This is how the offense could exploit a middle gap that is too wide.
So now let's discuss the other two mid-field defenders. Numbers 5 and 6 are known as "wings". They tend to keep their backs towards the sidelines, and are responsible for stopping the continuation throws downfield along their sideline.
If the disc is swung to the force sideline, the cup and mid-mid will be caught in a brief transitional period in which they will be vulnerable. See offensive cutters 4 and 5.
In this worse case scenario, it is up to the wing to stop the continuation down the line, and give the cup and mid time to catch up. Notice how 1 remains the mark, even though 3 was closest to the disc. This is essential for ensuring that down field throwing lanes are taken away.
The principal of needing to stop the continuation look also applies to the break side wing.
If the disc should somehow find its way to the break side...
It is essential for the wing to stop the line continuation cut, in order to allow for the mid-mid and cup to catch up.
Finally we come to the deep-deep or "monster". This is the defense's last line of resistance, as no one else will be behind them to provide help. As the disc gets swung from side to side, they need to assess the risk of the deep throw based on the down field cutters and the positioning of their wings.
The monster must be prepared to stop this deep throw to the force side, as their number 1 responsibility. See offensive player number 6.
If the offense is threatening 2 players deep, then the monster must give up the break side hammer look and cut off the force side cut before the disc is swung. Ideally, the breakside wing is aware enough to help with the hammer throw, since their primary responsibility is not to stop the swing, but rather the downfield continuation. Regardless, the monster needs to be vocal in calling for help from their wings. Unless it is a perfectly calm day or the handler has a wicked hammer, the throw to offensive player number 7 is high risk and what the defense wants the handler to attempt.
Again, everyone on defense should be shifting, as the disc is swung in the backfield.
If the disc moves to that break side, the defense must anticipate where the offense could go in order to make them vulnerable, and cut them off accordingly.
The monster has to respect the fact that number 7 on the offense could break it deep and is ready to help out over the top, but the monster is more concerned with the impending swing to the force side.
In this situation, the deep can let their break side wing know that they need help with the deep coverage, and sprint over to the force side, while encouraging the force side wing to come in on the offensive player number 5.
The initial continuation is covered, but as soon as the mid and cup have recovered, the deep and wing have to communicate the help on that side line.
The deep drops back, and the wing shifts back to the sideline.