The Government has decided to introduce the new scheme for the upliftment of poor.
Should it be "of the poor" or not?
Yes, the poor is correct.
The reason is that poor on its own is an adjective, which invites the question "poor what?". To turn it definitively into a noun it needs to be the poor.
Having said that, I did find a quote where just poor is used, in the Hindustan Times:
The Delhi government does not have an estimate of the number of poor living in the metropolis.
This indicates that it may be an acceptable Indian-English idiom.
As an aside, upliftment is awkward. Uplift is better; improvement or betterment better still.