Put diesel in the tank - what to do next?

Put 3 gal diesel in 2006 Chevy 2500 gas engine - added 20 gal gas (32 gal. tank -with the added gas it was about 3/4 full) drove 40 mi.,shut it off ad ran two other short trips (2 mi. or so) next morning it was smoking.& running albeit w/ not much pickup. Should I drain the tank, or simply fill it all the way up and drive it slowly without any trailer or full throttle load?

The short trips will foul the spark plugs, diesel fuel doesn’t vaporize, it will collect in the combustion chambers and on the spark plugs when the engine is cold. You probably experienced some misfiring when the engine was cold.

Diesel fuel will lower the octane value of the fuel in the tank, that shouldn’t matter under low load conditions.

At this point you are probably okay with filling it up. But I would think driving it unclouded, no trailer or cargo, at highway speeds, maybe even with O/D off, would work best.
But that is just an opinion, not based on extensive knowledge.