Is it possible to recover a damaged/corrupted micro SD card on Mac?

If other connected external storage media shows up in Disk Utility on your MacBook Pro, only the damaged/corrupted micro SD card doesn't appear there, it could be a dead SD card and can not be detected by macOS. Then, you could seek help from a local recovery service for the lost possibility.

A corrupted SD card could be caused by improper ejection, sudden interruption during data transfer, malware or virus infection, accumulated bad sector, etc. As long as the corrupted micro SD card can be recognized by your macOS, it is possible to recover data from it with SD card recovery software.

As you said, there is no problem with the connection between the SD card and your Mac including the SD card reader and the port, and the macOS could not be to blame given that it detects and mounts other connected external storage media as normal in Disk Utility. Then, the micro SD card may be heavily damaged and becomes unreadable. 

There is no third-party data recovery software that can recover damaged/corrupted SD card that is not showing up in Disk Utility. It won't show up in Finder, and the Desktop either, there is no way to access it at all. You are unable to restore the SD card by yourself. The last resort is to send it to a local repair, and it could cost a lot.