CPU sending and recieve Data?
That's why buffers are used. 

While the transfer is in progress the peripheral writes the data into a buffer and the cpu ignores it and just works on its own clock. 

Then when the transfer to the buffer is complete the peripheral will issue an interrupt (or other toggle a transfer complete pin) and the cpu will read from the buffer and if applicable let the next transfer start. 

The buffer used can be the RAM this is often referred to as Direct Memory Access. The peripheral is attached to the memory bus and can issue reads and writes to ram directly.