Try ferrite beads on the wires, or 100 ohm resistors in series with the transmitting/driving end (i.e., at the MCU, on the Arduino board, for CS, SCK and MOSI; at the ADC for MISO). Connect more grounds, and group all the wires together (multiple grounds/VCCs surrounding the CS/SCK/MOSI/MISO wires). For example, if you were using ribbon cable, it's preferred to make every other wire either VCC or GND.
Tim