I had a booking for KL via Singapore from Chennai. Is it possible to cancel the KL connection from Singapore at the last moment? The same carrier. Can I get my luggage at Singaore Airport?
You need to do that at latest when you check your luggage in; otherwise, it will have stickers to be checked through to the final destination, and that's where it will go.
You can typically cancel all segments you like to cancel backwards from the end, but not in the middle - in other words, when you cancel a segment, you lose all following segments, including a potential later return trip.
[the reason for that is the pricing structures of the airlines - connection flights are typically slightly cheaper than directs, and to avoid that people play the game, they have this rule. (real-world-)Example: I want to go from Orlando to Las Vegas. A direct flight round-trip costs 500 $. If I book Orlando to Salt Lake City with a stop in Vegas, it costs 400 $. So the obvious idea is to book Salt Lake City and then just leave the airport in Las Vegas. As they cannot force you to keep flying, that will work, and saves you 100 $ - but you lose the return ticket]