Ive read on wikipedia that Brion Gysin rediscovered the cut up technique when cutting something with an exactoknife on some news paper. This created strips where, if peeled back, might interrupt one section of one page with another.
If you take some text, and totally randomize it by words, the result is often too chaotic to be interesting. In my experience, the most interesting sentence chunks and word combination come with preserving sections of the source material. Below I will attempt to document some factors that can be tuned, mostly with preserving elements of the source material in mind.
When randomizing text, it might be beneficial to start by thinking of what are the basic fragments that will be shuffled. Some examples might be character, syllable, word, sentence fragment, sentence, or line. Generally, the larger the fragment size, the less chaotic and more coherent the output. Gysin's newspaper cut-ups might have looked most like character based fragments.
Keeping chunks of fragments from the source material together may create more coherent output. The smaller the chunk size, the more chaotic the output. Having a range in the size of chunks preserved from the source material may help create more interesting output.
When a text is split into chunks, each chunk can then have an opportunity to end up in an entirely new spot. A 100% chance of randomness would be equivalent to shuffling all the chunks and putting them back in a random order. But sometimes it might be useful to have several sequential chunks of the source material end up in the output. So decreasing this percentage would increase the probability of the a chunk of fragments being at the same spot it was in the source material.
Several texts can be blended with randomness to create another level of interest in the output. This also might be closer to what Brion Gysin was doing when cutting through newspapers. For instance, an article about a car accident might have been spliced with opinion piece on a new album.
It must be noted that with Gysin's newspaper cut up blends, sections of both source material were lost. Similar to introducing a tunable "Chance of Randomness", a chance that a chunk could be lost can also be introduced.
We have technology that wasn't available when Gysin was doing his cut ups. One possible additional method might be to keep the underlying skeleton of the sentence (the order of the verbs, nouns, etc) but to shuffle those individual word types. This would, in the end, have a Mad Libs type impact on the source material.