The only way an expansion tank can drain is for air behind the bladder to push it out. If your tank does not drain completely than it does not have enough air in it to displace the water inside.
If you have air in your water than your expansion tank needs to be replaced because the bladder has a hole in it.
To drain an expansion tank
First you need to drain the tank as far as it can go by itself. Next using a bicycle tire pump add air to the tank only until the water begins to flow out. Do not over pump the tank or you may ruin the bladder. Keep doing this until you are sure all of the water is out of the tank. Now to obtain the propper air pressure this can only be checked with the tank empty. Most well tanks use 30 to 38 PSI empty. Now it would be a good time to disinfect the storage tank with some bleach. Use an empty filter sump housing to introduce about a 1/4 cup of bleach into the tank you will need some valves to do this. Now rinse the tank by filling it and draining it sevrall times.