this is as much a people issue as a legal or formal governance issue.
Talk to your other Board members and significant investors, carefully, and see if they share your view of the problem person. If they don't you should consider your conclusions and think about whether you need to find a way to create a more productive relationship. More important, if they don't you may not have the votes to remove him and you could find your position compromised. Be careful of direct attacks or confrontation, at least until you're sure you have the backing of the other major players.
If they share your perspective they are potential allies who may be able to help approach the Board member and help work through the situation, minimizing disruption and finding a way to persuade him to leave the Board.