Slideoff DI is an advanced technique in Melee, utilising Automatic Smash DI when at the edge of the stage or a platform to immediately slide off and become actionable. It is particularly useful against platform tech chases which use moves other than grabs, as it will frequently allow for reversals out of those scenarios.

Most often, the input for Slideoff DI is to hold down on the C-stick and to the side on the control stick, facing the edge of the platform/stage. It is easiest to do it whilst right by the platform/stage edge, such as after a tech-roll.

Setchi slides off FatGoku's up air in a platform tech chase.
FatGoku attempts to use a Fox up-air to do a platform tech-chase on Setchi, but Setchi uses slideoff DI to escape and start his own tech-chase on the ground

Slideoff DI is easiest to do against moves that send the opponent at a roughly horizontal angle (like Sheik's forward aerial), or ones that send vertically at low percent (like Marth's up aerial). At higher percents, moves that send the opponent vertically will become impossible to Slideoff DI. Additionally, some moves, like Marth's up tilt, require slightly different inputs to correctly slideoff, and multi-hit moves, like Fox's up air, will require different DI inputs.

It should be noted that, on a per-character basis, there are frame windows during each tech-roll animation in which the character performing the tech-roll is unable perform Slideoff DI. A spreadsheet of each of these windows can be found here.

Sometimes, Slideoff DI is colloquially used to refer to a different technique, which is DI'ing a move so that you edge-cancel the knockdown animation and fall off the platform completely actionable.