Maximum grass lenght to cut

[color=Yellow]I understand you want to mow your grass to 3-4 inches not shorter. But how long do you let it get before you cut it so the mulch wont be too big? [color=Red][/color][/color]

Common wisdom in the lawn maintenance field is; you should never take more then 1/3 the lenght of the grass plant away. If you are cutting at 3inches, that means your clippings should be no more then 1inch long.
As for how quickly they will decompose? That will depend on what time of year it is, how much rain you get, etc.  And if you wind up getting little balls of clippings scattered over your lawn, just take a rake or blower and bust them up.