Try this…
instead of dragging the end boundary, to make the part smaller, Split it at the desired point, making sure you have enabled the following option in Preferences…
Preferences>Editing>MIDI>“Split MIDI Events”
This will indeed “chop off” the trailing notes (placing the remainder of those notes into the new Part after the Split), then all you have to do is delete the Part that was created after the split.
For info, the reason that notes continue after a Part boundary, is because what Cubase actually “records” isn’t two separate events (a note-on, followed by a note-off), but just a “note-on”, together with its length. This is to ensure that, if you do cut and then mute/delete a Part while a note is still playing, it won’t lose its eventual note-off (and then hang on forever!
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