There are some instances where you would like to cut up a beat repetitively as it is playing so the audience only hears one little part of it, like the kick or the snare (usually while nothing else is in the mix). This isn't cutting, or transforming but deconstructing, because you never touch or manipulate the record taht is playing. You only use the mixer to create the effect by bring the sound in and out and equalizing it live. Here's a visual example:

In this case only the kick and all the sounds happening at the same time as the kick will be heard. The idea is simple in principle, however some djs may have noticed that if you do this for an extended period of time you risk loosing the tempo of the track and may start to miss the beat. The effect usually gets worse the longer you do it, or if someone is talking to you.

When you attempt this effect, be sure to keep your headphones on and have the track in cue, this is good especially for performances where the sound system output is sligthly delayed from what you are cueing. stop listening to the sound system and instead concentrate on the headphone cue. you will not hear your fader moves in the cue but it's not important. Let the cueing be your guide and go through the motions. Just concentrate on matching your movements to the beat in the headphones.

Don't use the line/phono selector to cut the sound in and out. Instead use the input fader on the mixer to do the on/off effect. The reason for this is that if you use any "cut" buttons you might also loose the track in your cueing. By using the fader you deconstruct the track After cueing so that no matter how much you play with the fader you never actually loose the whole track in your headphones. So you always have a reference point for what the rythm is doing. This way you can decon a track for as long as you want without ever loosing track of the beat. This way it's also a lot easier to do "shifts" too.

A shift is when you go from letting through one part of the beat for another. For example : Letting the kick out for 4 bars then switching to the open hi hat for 4 bars then switching to the snare (and so on).When you get good enough you can create alternative signatures for the beat live without ever touching the record. Just remember to position yourself properly as to not work or twist the fader. You are going to be doing a lot of back and forth motions on whatever fader you use so place your hand acordingly, that is in a way that the fader will hold the least resistance to your movement. Now you can deconstruct to your heart's content.