s4 mini SD card makes battery drains fast?
There are known issues with certain SD cards causing some read/write errors which prevent your phone from entering the deep sleep state. This causes your phone to drain battery fairly quickly as compared to a phone which goes into deep sleep when not in use. 

You should update your phone as certain kernels have also been known to fix battery drain issues. If it doesn't help, consider changing to another sd card from another manufacturer.