He cannot stop Trump from adjourning both chambers but he can limit the length of the adjournment . Both the House and the Senate must agree as to the time of the adjournment. The problem is they must be adjourned for 10 days or more for the President to make appointments. and the Senate has passed a bill that limits the adjournment to 4 days or less I believe to avoid Presidential Recess Appointments.

I am pretty sure Trump knew what Mitch would do and has a remedy in mind to achieve his goal. If Trump has evidence of Mitch being compromised he will use it to force him to comply. Perhaps that will be the Trump card.