Note: this article also applies to the Korg M50.
You want to erase the notes from only a portion of a measure, or move (shift) the notes from one portion of a measure to another specific beat:tick location. The track editor for the M3's internal sequencer (SEQ page P6: Track Edit) seems to perform operations only on entire measures when using the "Erase Measure", "Move Measure", and "Copy Measure" commands.
This is accomplished using the menu command Shift/Erase Notes, which is described in detail on page 301 of the M3 Parameter Guide. In the resulting dialog, you can specify a starting and ending measure, beat and tick. Since the start and end measure can be the same, you can erase/shift the tiniest portion of a measure this way. This command only works on note data, however. But you can erase only a range of notes if you wish, like the left hand of a piano part. If you specify the full range of notes, then you can erase/shift all notes from the specified measures or portion of a measure.
If you also want to erase or shift corresponding CC data in the same area, you do this with the menu command Erase Control Data, which is described on page 300 of the Parameter guide. This has a similar interface and can operate on any or all controllers, pitch bend data and more, with surgical precision.
Both commands let you specify the precise measure:beat:tick range to erase or move.