Hey!
I built a device that measures speed by GPS, displays it on a screen, and saves it to a micro SD.
If I check only the on-screen display everything works great, If I check the data retention to micro SD, everything works great. But when I connect them both, the screen works very slowly (20 times slower) and the micro SD fails to save data.
I suspect that this may be happening because the screen and micro SD are connected to the ARDUINO with SPI.
I will be happy to suggest how to fix 
Show us the wiring. That uSD card needs 5V to 3.3V buffering, it does not appear to have any on it.
I usually use a cd74HC4050 powered from 3.3V for 5V to 3.3V on SCK, MISO, and Chip select, and then a part like 74HC125 to bring 3.3V MISO back to 5V, with gate driven from the unbuffered chip select. That also keeps the uSD MISO off the SPI bus while the screen is active, some SD cards are known to be not totally bus friendly.
uSD cards can also need a lot of current when being accessed, what are you using for a 3.3V supply? The 150mA from an Arduino regulator may not be enough.
The screen:
All the information in the link to the screen above.
Micro SD:
DO to pin 50, DI to pin 51, SCK to pin 52, CS to pin 53, VCC to a Regulator GND to GND.
And you have a separate CS for the uSD, yes?
CrossRoads:
And you have a separate CS for the uSD, yes?
Yes, the CS of the micro SD in pin 53, and the CS of the screen in pin 10