When you turn off the ignition and the engine sputters on, it’s called dieseling. High-octane gas may help; if not, look for a mechanical fault.
Check the engine idle speed, for which you’ll need a tachometer. If the idle speed is too high, a carburetor adjustment may cure dieseling. If the carburetor has a solenoid, its plunger may not be retracting when you turn off the ignition (have a helper look). If it is not retracting, replace the solenoid.
The idle may be too high because the throttle linkage is sticking. With the engine running, push the linkage. If the idle drops, the linkage apparently is sticking. Spray it with aerosol solvent to remove dirt.
If it still sticks, install a new throttle return spring. Disconnect the old spring. The universal replacement spring will have straight ends rather than hooks.
Make a hook on the straight wire at one end and engage it in the less accessible slot, usually on the throttle linkage. Then extend the spring and, exerting just a slight bit of tension, line up the other end with the slot in the fixed bracket. Use pliers to form a hook and fit it into the slot. Clip off excess wire from the ends with cutting pliers.
Other causes
Check the temperature gauge. If the engine is running hot, suspect a faulty thermostat or try flushing the cooling system.
The ignition timing maybe too far advanced. If you have a timing light, you can check this, following the instructions with the timing light and using the specifications on your under-hood tune-up decal.
Certain cars have an antidieseling relay, which briefly triggers the air conditioning compressor when you turn off the engine. If the compressor does not click on when you turn off the ignition, have a mechanic check this possibility. Cars that use such relays include Chrysler cars with 1.7 and 2.2-liter engines, General Motors cars with the 2.5-liter 4-cylinder, and some Fords with 3.8-liter V-6s.