Where is the ground reference when using a thermocouple?
You do need to connect the bias pin to the -T input to set up the input correctly: -



You also need to run both chips from a common 0 volt rail (AGND on MAX31856 connects to Vss on ADG707 multiplexer).

You also need to ensure that your address timing is correct and that you give the MAX31856 enough time for the input/multiplexer to settle prior to reading the value. Sometimes, on open circuit thermocouple inputs to a multiplexer like this, it can take a little longer to settle.