If you are using 11-13 these are on SPI1 not SPI.
Not sure if the simple SD library supports SPI1 or not. I know there have been other threads talking about as option swapping, SP and SPI1.
Red sort of arrow pointing toward SPI pins
Blue circled the SPI1 object pins.
With SDFat you can specify SPI1.
Where:
#include <SdFat.h>
...
#define SD_CONFIG SdSpiConfig(SD_CS_PIN, DEDICATED_SPI, SPI_CLOCK,&SPI1)
...
if (SD.begin(SdSpiConfig)) {