If your son has been dismissed from the school as a consequence of this disclosure of his disability, then the school may be violating your son's civil rights. If they receive any federal funds (for scholarships or grants, for example) the administrators of this school may have put themselves in very hot water by behaving in such an obviously prejudicial manner. Section 504 of the Rehabilitation Acts of 1973 expressly states, "No otherwise qualified individual with a disability in the United States, as defined in section 706 (8) of this title, shall, solely by reason of his or her disability, be excluded from the participation in, be denied the benefits of, or be subjected to discrimination under any program or activity receiving Federal financial assistance." You should indeed contact an attorney; you can also file a complaint with your state's Office of Civil Rights and they will investigate the case.
In all fairness, let's try to look at this from the school's point of view. You said that they "accepted him with the LDs." They may be saying that they have to use an extraordinary amount of resources, or that they may lack the specialized expertise to help your son keep up with the demands of school. In their advertising materials or during the interview, did they expressly state that they do not have special resources to meet the needs of students with learning disabilities? If so, this "disclaimer" may be sufficient to justify their decision to dismiss your son (as much as we might find this distasteful, especially at mid-year).
The school may also be "frightened" by the LD label, thinking that now that your son's educational difficulties have a formal name, his teachers should not be trying to work with him, in case their untrained efforts might prove harmful. If so, they might benefit from consulting with a professional trained in learning disabilities, who may determine that the school is actually "doing the right thing" intuitively or programmatically. What they do at this school to meet the needs of all students might be just the thing your child needs. Remember: Good LD programming can't hurt anybody. Not providing it can clearly hurt students with LD. If they really can't provide it, or if your son always feels like he's in over his head, you probably don't want him to be there.