I have pulled a few mushroom anchors in the past. After doing 10 or 12, lets just say going out and buying your own gets to be attractive.
First, most mushrooms will be between 150 and 500 lbs. This will depend on the boat size and bottom type sand, rock, mud, ect.
In mooring fields the local harbor master or yacht club should be contacted. They know there are a lot of lost gear out there and they just may make a deal, you go and mark 5 or 6 anchors for them, and you get to keep one of them If they are really nice, they might pull it for you with a mooring scow. What these are, are flat floats with about 2,000 lbs of floatation, the ones I have used have a hole in the center with a tripod and chain fall on it. At low tide they center over the mushroom to be pulled, hook up as far down as they can, and take as much tension as they can. Then go back to the dock and let the rising tide do the work of pulling for them over the next 6 hours.
Many newer mushrooms will have a trip chain or cable. This trip should go from an eye at the edge of the disk up to the shackle. When it is time to pull the mushroom, a line is attached to the trip and tension is put on the side of the disk to pull it out sideways. Much easier then a straight upward pull lifting all the mud and a lot of bottom suction.
But if there is now trip or if you want to do it the hard way, The worst case is mud, here is how Iv done it: put 3-4 times the weight you think the mushroom is. Now slowly start to dig the mud off the top of the mushroom. The shank of the mushroom is almost always tilted, start on the up side of the tilt so that as the mud is removed the shank should move straight up and down. Now comes the interesting part, there is a lot of suction holding the anchor down, and a lot of lift trying to pull it up; Put one hand on the edge of the mushroom disk in front of your face. This is so that when the suction breaks, the disk doesnt break your jaw as it passes by on the way up. Now, use you other hand to dig under the disk and work it quickly back and forth to gell the mud and let water under it. This should break the suction and the anchor should go quickly to the surface.
Again, when it starts to go, you have to be out of the way, it will go very fast.