git rm

using (var repo = new Repository("<repoPath>"))
{
    // Removes the file. Path must be in Posix format (using '/' as path separator)
    repo.Index.Remove("<file>");
}

using (var repo = new Repository("<repoPath>"))
{
    // Create the committer's signature and commit
    Signature author = new Signature("Author", "@Author", DateTime.Now);
    Signature committer = author;

    // Remove the file. Path must be in Posix format (using '/' as path separator)
    repo.Index.Remove("<file>");

    // Commit to the repository
    Commit commit = repo.Commit(message, author, committer);
}