This would be a new application of the Faithful Execution clause, but there is ample legal precedent for the other branches of our government to review and sanction the Chief Executive for a failure to abide by Presidential obligations. Presidents Truman and Nixon bore the scars of such recent battles.
If Trump does refuse to speak to Mueller, he risks a grand jury subpoena. Two previous Presidents went that route and neither Clinton nor Nixon fared very well in the courts. The President would then likely have to testify under oath and incur substantial risk of perjury and self-incrimination. Or he could claim a Fifth Amendment right to avoid answering Mueller’s questions by asserting his testimony would tend to incriminate him. (In which case: Yikes… The Donald morphs into The Don.)