It would help to know which model of Thetford loo you've got.
If it's an electrical flush, then I don't know the problem, but on the assumption that it's a hand operated one (most are)....read on.
By the sound of it, you have a problem with the flush mechanism, which does not have anything to do with the removable cassette. Therefore removing and stripping down the cassette unit is unlikely to help.
Thetford loos come in two parts.
The removable part is the cassette, which lifts out of the side locker,when full of waste, for emptying and cleaning. These are pretty foolproof, and work well, so long as they are looked after, and the seals lubricated occasionally.
The tank unit,however, is built into the structure of the caravan, and comprises the seat,lid, flush knob and mechanism, and release valve for emptying the contents of the bowl into the cassette.
If you have a problem with the flush mechanism, then you will have to investigate further, from inside the caravan.
I've not had this problem, but Thetford may be able to send you details/ diagrams of how to get to the flush mechanism, and repair it. They are one of the most helpful of caravan accessory manufacturers.
If you have a Thetford Manual for the loo you've got, then it will have this information in it.
They also have an excellent website, and you could email them.
Hope this helps you.