I faced a similar problem when working on a group project for my degree.
The first thing I'd question is if you actually have the authority to remove people from the team, especially if the project has been underway for more than a year. Are you in a supervisory position? Do the terms of your assignment allow you to democratically remove other team members? If you decide to go down this route, fully consider all possible consequences, as the people being 'removed' will presumably object to this, and might take actions against the other team members in response.
Also, consider that regardless of other outcomes, the assignment will definitely look like a failure in at least one respect ('person management', 'good teamworking' etc) if the team is broken up in this way.
And - although it's difficult when some people are clearly doing far more work than others - in the absence of objective proof, I think you have to give people the benefit of the doubt if they claim to have personal problems. If nothing else, consider how bad it will look if you remove someone from the team, and they then provide evidence of (eg) health issues or bereavement to your academic supervisor.
With all that in mind, our solution was to call a 'clear the air' meeting where everyone discussed their concerns, with an emphasis on how to solve the problem, rather than blame or accusation. We also agreed that:
- As far as practically possible, the work was reassigned into independent 'chunks', and poorly-performing members were teamed together when assigning the chunks. That way, we ensured that continued failure by one or two people couldn't jeopardise the entire project; their section might end up missing, but other parts could proceed unaffacted. This also gave them the motive and opportunity to 'pull their fingers out', as it increased transparency regarding who was responsible for chunks that were delivered (or weren't).
- At the end of the project, every group member provided an evaluation of the group as a whole, and of each member's contribution to the project, as part of the submission. This gave us an opportunity to give credit where it was due, and allowed us the chance to explain to our academic supervisor why certain parts were more successful than others.
The benefits of the above were that it kept the team together (which is a success in itself), that it treated all members of the team equally (everyone still had the same opportunity to succeed, if they wanted to, but with increased individual accountability; and the same opportunity to critique other members at the end), that it did not give anyone cause for grievance or 'appeal' etc, and that (IMHO) it was the most morally correct solution.
The outcome was that some (although not all) of the lesser-performing members improved considerably, the project was broadly successful (ie in terms of the specific 'academic' targets), and got a good mark. Also, it greatly reduced the personal tensions within the team for the remainder of the project.
I'm not sure if all the above will be relevant to your particular situation, but hopefully it provides some points to consider, at least. Good luck!