The first time that I tried to get an SD card working with CubeMX I found a most interesting affair - not particularly complicated, but definitely a little fiddly.
2020 edit: There is a more detailed and up to date version of this post. Use it instead.
At any rate, the goal was to get a STM32CubeMX-generated system integrated with FatFs middleware managing an SPI-connected MMC/SD memory card.
The project was initially created in CubeMX, and then code written by ChaN was ported to the CubeMX HAL.
If you’re interested, the project github has the relevant details (2020 edit: this may be out of date) and interesting files, including a SPI driver at Src/user_diskio_spi.c and Inc/user_diskio_spi.h which should be usable in any CubeMX project (although the SPI handle hspi1 may need to be changed depending on your requirements).
The CubeMX project file is nucleo-sdcard.ioc in the root directory. You can load this with CubeMX and change any of the settings and regenerate without affecting any of the code in this code base.