Not possible. If you don't board the first leg (TPE-HKG) the rest of your itinerary is cancelled.
Go to a TA in HKG and you should be able to get it for much cheaper. Search 'nanda' in this forum to see why HKG-India is so expensive when you book online yourself.
If finding a local TA is not an option do what was suggested above - buy yourself a one-way HKG-TPE.