how old is the pipe, is it metal or pvc? If the pipe is metal and very old, you will probably need to replace all the piping under the sink which is really only about three sections. Normally an old metal pipe's joints and joint nuts are so old and so brittle that they will crumble when any force is applied to them. Sometimes the nuts or nut will not budge.
I would consider removing all the pipes under the sink with proper force and then replace them with pvc pipes. you only have three sections, on down pipe from the sink drain pipe, then the P trap pipe then the pipe from the P to the wall drain pipe. This should not cost more than $15 and the hardest part is removing the old. You might need a hax saw to modify the lengths of the new pvc piping.