If I take down chimney, will it solve damp problem?

You need to pin point the area of the dampness or leak it may be the flashing, may need brick tuck pointing and water proofing,you may have rotted wood around the area causing the problem. If the chimney is part of the structure then you will also be redoing the siding or whatever exterior finish you have and if you only do that spot it will always look like a repair! You will also need to do interior repairs if the chimney is in a finished part of the house Good luck