Normally, shuffling reduces your speed by an amount proportional to your initial speed (see JSRF Speeds Chart). A negative shuffle utilizes a particular setup to cause a shuffle to increase your speed instead, slowly building up to extreme levels.
The only known way to do a negative shuffle is during a mission against a CPU player, e.g. City Rush: you must skate sufficiently ahead of your opponent, turn around and skate backwards into them. If you shuffle a little before the point of impact, you will be knocked down and will emerge into a negative shuffle. In that state, your speed will continue rising until you exit the shuffle.
Negative Shuffle currently has two possible uses in runs: Beat Race and Death Ball vs. Doom Riders. In the Beat race, negative shuffle can save 5 seconds when done safely or upwards of 8 seconds when done with a faster setup. The death ball setup is currently not consistent enough to be viable as passing the corner after the wallrides section while preserving is very difficult, as seen at the end of the top video.