multiple connection with ISP Pin at Arduino Micro
Each SPI device must have a separate device/slave select pin. The device must disconnect (high impedance state) when not selected. The SD shield will have a level shifter. It may not correctly disconnect from MISO. 

Depending on what libraries you are using you might also need to check that they set the SPI hardware attributes correctly (clock, mode, etc). 

For more help please post code and references to the shields and libraries.

Cheers!