Miele CM6310 coffee brew unit fitting snapped off. The coffee flow was slowing down and finally halted altogether, with wet grounds in the waste. Found a fitting that snapped off.

Just so you know, we are Fixya, we aren't Miele.

You need a seal kit, basically a set of o-rings for the brew head. This machine ends up in Fixya far too frequently!

https://www.google.com/search?q=miele+cva+4066+replacement+parts

..

try flushing with vinegar

On the left side of the brew unit there should be a metal wire that is bent in the shape of a U that scrapes the grounds off the top of the brewing chamber - the puck then should slide down a small chute that is the shape of a W - into the waste container. Sometimes the Chute can be found installed upside down - shape of an M - it is easily reversed if that is the case

Have you changed your type of coffee beans or grind setting recently? First of all I would recommend removing and cleaning the brew unit thoroughly (as per cleaning instructions) to eliminate any cleaning issue here...
This is sounds like the flush valve is not working correctly. The flush valve ensures that all unused liquid in tubes is flushed into the driptray and that all solid coffee (dry pellet) goes from the brew chamber into the waste container. At the end of the coffee cycle when the pump stops running, the piston in the brew unit usually moves one last cycle and squeezes the coffee pellet in the chamber one last time and the flush valve operates so that all waste liquid is flushed from the coffee pellet to the drip tray. If your pellet is wet, then this final flush is not working. There may be a blockage in your flush tube or the flush valve may be blocked. These usually block up if you don't run a cleaning tablet through the machine regularly.
My advice is to remove the driptray grill and check that the tubes running into the tray from the brew unit are not accidentally squeezed closed or blocked. Good luck.

The standard instructions are ... remove the waste container, water container & ground coffee container. On the front of the Brew Unit is a vertical black lever with a grey press button at bottom. Press this button and turn the lever clockwise. Then press the release catch that holds the brew unit as base and pull the brew unit. If Brew Unit is still stuck then its likely that the Unit State is not in the 'home position' and if this has occurred then its likely that that an error code would be showing. Regards

What you see in the waste tank dry coffe powder?

Have you Cleaned the Brew unit? The descale Tablets are to clean and descale the internal plumbing - the cleaning tablets are to remove the oils from the brew unit. If clogged the water will not flow through , instead it will dump into the drip tray.

If the Hot water and the steam function work fine - then I would say the water system and heaters are good. Are the grounds being dumped in the waste dry? I would guess so. The brew unit drive sounds to be the issue - it has a valve on it that dumps the water to waste if the pressure is to great - the waste valve sometimes gets stuck, but in your scenario it sounds as if the brew unit is not being driven to full compression (the clicking sound) and if that is the case the operation is cancelled. One thing you may try - set the grind to coarse and try a small cup - this is easier on the drive and may work - showing the Valve is good and the brew unit drive is starting to weaken.
Hope that helps

The brew unit has lose parts on left-hand-side, wiggle them up and down. Put the waste unit back, switch off the machine and then turn it on (pull the cord). It worked for me!!!