I don’t know how the arduino libraries work but its controlled in the PHYCFGR register at 0x002E offset.
To power down the PHY you need to modify the OPMDC bits to 110 the powered down PHY mode, also set the OPMDC bit so the PMODE pins do not control the power mode. I would also set the RST bit of the register at this time.
Once this is done you need to reset the PHY to make the change take effect. This is done by clearing the RST bit in the PHYCFG register. I read the whole register, clear the MSB (RST bit) and then write it back.
With everything enabled and no cable connected I see 64mA, with the PHY powered down I see 31mA at 3.3V and room temperature.
The W5500 data sheet has a typical power consumption value of 13mA but I haven’t managed to achieve this.
If anyone has any real world current consumption numbers for the power down mode I would appreciate them posting them. I prefer my chip data sheets to have max values, even if its a somewhat high test limit.