For reference, if Didymos were on a collision course with earth, we'd need to our interceptor to hit it about 16,000 years prior to impact to get it to miss Earth, or more realistically a substantially larger kinetic impactor/ swarm of impactors.
You need to impart kinetic energy and quite literally push the rock away. The only reasonable way to do that is throwing inert kinetic projectiles.
Think about starting a Newton's Cradle by lighting a firecracker under it instead of dropping one of the balls. Technically the firecracker has an order of magnitude more energy, but basically none of it is translated into 'useful' kinetic motion.
https://www.universetoday.com/articles/nuclear-detonations-c...