can sell, why not? Ive done the same thing but once it is handed over to the new owner, you will need a place to stay.

my steps in my own case -
1. bought a new place with 10% deposit for new property which needed 3 years to complete.
2. start selling the current house which i was living in. it took quite awhile like 1.5 years or bit more.
3. after hand over to new owner I rented another place and moved out
4. waits for new place to be completed while renting