If we knew that a near-Earth asteroid (NEA) was headed for Earth could we deflect it?

Seeking to find out is the Double Asteroid Redirection Test (DART), a mission from NASA and the European Space Agency (ESA) to smash a 500kg spacecraft into binary asteroid 65,803 Didymos and its moonlet Dimorphos (also called, rather cutely, “Didymoon.”)

The idea is that by creating a “kinetic deflection” on Dimorphos it will ever so slightly change the trajectory of both objects.