You have your car towed to a repair station where they will bleed the brake fluid and grease out of the brake system, and replace them with good, clean brake fluid.
There could be several reasons such as, you forgot to release the e-brake and drove the vehicle with the e-brake on, or a grease seal went bad and grease is getting onto the hot brake drum or brake rotor, or brake fluid from a leaky wheel cylinder or caliper is getting onto the hot brake drum or brake rotor.
I don't know what you mean by clutch grease, but the clutch master cylinder uses dot 3 brake fluid as a hydraulic.
Could be a leaky grease seal or a leaky wheel cylinder in the right wheel and the grease/fluid is getting on the brake shoes. Could also be that the brakes are not adjusted properly.
Drain the brake fluid from the brake master cylinder reservoir. Remove the wiring harness from the brake cylinder. Remove the brake lines. Remove the brake cylinder retaining nuts. Reverse the process to install the new master brake cylinder.
NO! No...no...no...! Do not put any grease on your brake discs, copper grease is used to put on the 'back' of the brake pads (not the part of the pad that comes into contact with the disc).
Master Cylinder internal seals are failing. Replace the Master Cylinder before you have an accident when it fails permanently.
Several things could be the cause. You could have an emergency brake not releasing. You could have a brake hose internally collapsed or a leaking wheel cylinder. A defective grease seal letting grease get on the linings are some possibilities.
What cylinder? Master (brake) cylinder? Rear Brake cylinder? Lock cylinder?
Usually you get a big mess of brake fluid all over everything around it.
A blown out rear axle seal will cause grease to leak out into the brake drums
Master cylinder or drum brake (hydraulic slave) wheel cylinder or disc brake caliper cylinder? drum brake shoes rear
The brake cylinder may not compress properly due to air bubbles in the brake fluid, a leak in the brake system, or a malfunctioning brake cylinder.