One big problem with cutting the lid from a closed box on a tablesaw is that the box and lid become more unstable as subsequent cuts are made.
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One big problem with cutting the lid from a closed box on a tablesaw is that the box and lid become more unstable as subsequent cuts are made. The bigger the box, the more potential for binding and gouging and the more dangerous the operation becomes for the woodworker.

For several years I've made boxes as small as 4" square and 2" deep for jewelry and other pieces and as large as 16x24x48" for blankets and toys.

For safe, stable lid cuts, I raise the saw blade to the correct cutting height (slightly greater than the stock thickness) and cut the two long sides first. Next, I apply a small amount of hotmelt glue to each kerf where shown in the inset illustration at top. I then make the end cuts and separate the box and lid by cutting the glue with a sharp utility knife. I also use the knife to peel or shave away the glue before sanding to remove the saw marks.
—John Ash, Lockport, Ill.