How can I remove clothing wrapped around bottom of agitator?

This issue could be caused by a number of things. It is possible that the clothes are not properly balanced in the wash drum, causing them to wrap around the agitator. It could also be a problem with the agitator itself, or with the transmission.

That does not sound good. New dogs sound great, but you must get to the bottom of why the clothes are becoming twisted on the agitator. Usually not enough WATER. Think loose flow of clothes submerged.
Long story short, you cannot jam pack this machine. Less clothes, more water, will equal long life.
Be sure that the mating teeth for the dogs, is not damaged. Slipping here would make loud noise.
More water, less clothes.

Here is a video on how to change a part that could be part of the problem, the video shows how to remove the agitator so that you can remove the clothing that is jamming the machine, http://www.repairclinic.com/PartDetail/Whirlpool-Washing-Machine-Agitator-Repair-Kit/285809/470910?modelNumber=WTW4800XQ1&ss=a11b5d956381&mr=1

When loading the machine, load towels, sheets or jeans with an accordion fold instead of putting the laundry in a circle around the agitator. It helps to put the clothes in at the twelve o'clock position, then six o'clock, then nine o'clock and then three o'clock. Repeat this sequence until the washer is full.
The laundry can circulate much better and get cleaner too.

clothes wrap around agitator. making clunking noise only while agitator is working

Sounds like your agitator is not assembled correctly. It should not have things getting stuck constantly and it should definitely NOT be so easy to remove. Feel around the bottom edge of your agitator. If there is more than a 1/8 - 1/4 inch gap (roughly), it's not being snapped all the way down. Take a towel and fold it to where it is nice and fluffy. Lay it over the top of the cone part of your agitator. Get a hammer and hammer over the towel (as not to damage the agitator top). A rubber mallet could also be used. Tap firmly until you hear a click or until the gap between the agitator and wash tub reach 1/4 -1/8 of an inch. This should solve the problem.

Hope this info was helpful to you. Good Luck!

If The washer won't agitate
Check to make sure no clothing got wrapped around the agitator. Check the lid switch, timer, and drive belt, other potential causes, such as a bad transmission or bad agitate/spin solenoid, but they are much more involved.
if the washer won't spin, the lid switch, timer, drive belt, transmission, or agitate/spin solenoid could be the cause here as well. Sometimes if the load is unbalanced or too heavy, the washer won't spin. Take some of the clothes out and try the spin cycle again with a lighter load.

Here are the steps to replace the agitator.
1: Take the fabric softener dispenser off and pry off the agitator lid.
2: Use a socket wrench with an extension bar to remove the stud and seal.
3: Remove the agitator top and bottom.
4: Check the agitator clutch assembly (located in the agitator top) for excessive wear.
5: To replace, just reverse the directions.

Hi,
If this a whirlpool brand washer, there are sone parts bad in the agitator it's self. These parts are called dogs and they make the agitator rachet so that the top half only goes one direction. Does this sound like what you are experiencing? If so, let me know and I can assist you further.

Thanks
Vic

GE spacemaker washing machine . cloths wrap around the agitator . how can i solve this problem .

some fabrics are known to do that you have on wrong cycle setting there should be a setting for delicates and clothing and blankets and things when loaded to close to agitator will attract each other together so its wise when loading machine load in a circle leveled out till desired fullness away from agitator they shouldnt attract as much