There are two ways you can use avios when making bookings.

One is part pay with avios where you are making a cash booking and taking advantage of an offer to reduce the cash due by using some avios. This is called part pay with avios (which is what you are asking about), and using the avios has no effect on your tier point and avios earning. So if you were booking a short haul club europe flight earning 40 tier points, you would earn that regardless of using avios to reduce the cash cost.

The other use is avios & money which is where you make a reward booking and the reduce the amount of avios required by paying a cash supplement - reward bookings do not earn TP or avios, and paying extra cash to reduce the avios needed does not change that.

For part pay with avios you can only do that for BA and AA flights. In any case, BA won't sell you a standalone TPE-PEK flight on CX so there would be no option to book this as a revenue ticket through BA.

For avios & money you can book rewards using avios on CX and pay more cash to reduce the avios required, but reward flights do not earn avios or TPs and paying extra cash wouldn't change that.

So basically I don't see there is a way to book your CX flight partly using avios and earning TPs.