How do I cut a plastic box without shattering the plastic?

[robinbanks]

If you're going to cut it, warm it first. Grinding or melting brings its own heat

 

[Odds]

No , no pressure is required to melt .

Yes, i get that.
What i'm looking for is a simile to describe how much pressure is best -
Something like: 'a hot knife through butter', or 'it's like cutting cold fruit cake'.

 

[Safety First]

Depending on finish required, for the edges and the speed of delivery, I would use a multitool with grout remover (diamonds) or stitch drill with Dremel and 'pop -pop-pop' connect the dots cutting little by little with Stanley knife.

Melting-stinky and horrible. Angle grinder hard to stop it melting and dangerous.

 

[foxhole]

Yes, i get that.
What i'm looking for is a simile to describe how much pressure is best -
Something like: 'a hot knife through butter', or 'it's like cutting cold fruit cake'.

Hot knife thru butter would be a good comparison .

 

[opps]

Surely, whichever technique you use, the integrity of the lip will be compromised? Pick up the box when loaded and it may well split.

 

[Brigadier]

For what purpose are you cutting the slot out?

Might you be better drilling a hole (diameter equal to the width of the slot) in the centre of the lid?