The Deek Robot Micro is almost an exact replica of the "Sparkfun Arduino Pro Micro" the only the SPI pins differ, which would normally be on 11, 12, and 13. On the Pro Micro they are on the 14, 15 and 16 pins.
I2C is on pins 2 (SDA) and 3 (SCL) not A4 and A5
SPI is on pins 14 (MISO), 15 (SCK) and 16 (MOSI)
There are four analog inputs (A0-A3) rather than (A0-A5)
there are 14 digital I/O lines, RX1, TX0, D2-D10, D14-D16
16MHz, 5 volt, 36mA draw current, 14 digital pins, ATmega32U4 MCU - Deek-Robot Pro Micro
So you have to change a few pins over to this configuration but it should work once you do this.
For the data logger the pin outs are as follows;
D10 - chip select
D11 - SPI MOSI
D12 - SPI MISO
D13 - SPI SCK
(from the Chinese website that makes them) Data logging shield V1.0 (things are different for the Deek Robot versions but there are no pin out data sheets on the net that are in English by the looks of things).