Is it legal to pull a project from under the executive producer?

The answer will depend entirely on the terms of the executive producer's employment contract. It will spell out the circumstances under which the EP can be terminated.

The Executive Producer is the person who provides or arranges financing. The documentary is completed. Now the director says he would like to pull the project out from under the Executive Producer. The Executive Producer has already done his or her job and done it well, since the film has been completed. I do not even understand what the director might mean, other than that the director might be trying to get the film production as a whole to renege on its financial agreements and contracts. The Executive Producer is the person who has arranged for the financing, and has arranged for people to be paid back, arranged for distribution and for the whole financing and operation to be legal and secure. The director sounds very confused.

It really depends on what, if any, contracts exist and what those contracts say. Among other things, in this kind of situation, it's important, among other things, to make sure that the whole project doesn't collapse under the weight of a dispute between the interested parties. It's also important to approach the situation in a creatively strategic way, and it's not really possible to do that without evaluating the contracts and determining what your legal rights and obligations are.