I'm using a mixer chip with 8 leads, 4 leads are GND
My question is, should I connect the 4 GND leads to my circuit board GND or it is enough to connect only one of the 4 GND leads to the board?
They likely are but, particularly for high frequencies, you want the Gounod connection to be as low impedance as possible, so they connect the chip to ground at more than one spot.