Switch power on/off when SD card is inserted/removed in slot
Logic circuits rely on good ground connections to function properly and putting anything in the way is going to lead to problems. Sensing current on the supply pins has a better chance of working, as they're generally more tolerant of a wider range of voltage.
But there's a far better way to achieve what you want to do - use an SD socket with a built in switch to detect card insertion, like this one:

Most SD card sockets have a similar facility, it shouldn't be hard to find one.