Circuit design for short-circuting outputs when needed
A reference to a data sheet would be very helpful.

Using a multiplexer for shorting is a potentially good solution. You need to determine what the impedance of the sensor is under short circuit conditions and what residual voltage be present when the chosen multiplexer is used. 

If you want a precision measurement, a well defined and very low resistance short may be required. If the polarity of the pins to be shorted is always the same then using a MOSFET across the pins with gate driven on as required will short the sensor. Choosing a very low Rdson MOSFET will give a lower shorting resistance than is available from most multiplexers. 

If the sensor output can be of either polarity you could use two MOSFETS in series opposed polarity. eg 2 x NChannels, join sources , join gates, connect two drains to sensor pins. [Possibly optional: Connect high value resistor gates to sources (say 1 megohm +) to hold FETS off usually.] Drive gates with input resistor - saya 1 megohm+. Drive low = off. drive high = shorted. Drive voltage and MOSFET ratings to suit.