Hi there, based on your description, I suggest you do a basic troubleshooting first. You can check your SD card on another computer, change the USB cable, USB port, or SD card adapter, reset the USB port, and more.
Specifically, you can insert the SD card into another computer, or try an alternative USB cable, USB port, or SD card adapter to connect the SD card and your device. Or, resetting System Management Controller is workable also.
If the basic fixes fail to make your SD card readable on your Mac, then move on and try the following solutions.
Solution 1: Update the drivers on your Mac
An outdated driver likely brings you the notification which reads "The card you inserted is not readable by this computer." You can check the drivers on your Mac and update them via the following steps:
Step 1: Go to the Apple menu and select System Preferences.
Step 2: Click Software Update and then check for any available updates for your system and applications.
Solution 2: Recover data via software and replace a new SD card
If all mentioned above fixes are unable to fix the issue that SD is card not readable, I assert that you need iBoysoft Data Recovery Software to have a file recovery and then replace a new SD card for storage work.
iBoysoft Data Recovery Software is highly recommended for it can scan all your files and data on your SD card comprehensively, including MST files, Word documents, FLV files, Excel files, images, Sketch files, HEIC files, etc.
You can download and have a free scan first. After making sure that the scan is successful, you can purchase the recovery technology then.
Step 1: Free download and install iBoysoft Data Recovery for Mac.
Step 2: Connect the SD card to your Mac, then open the data recovery tool from the Applications folder.
Step 3: Select the SD card that you wish to scan and click "Search for Lost Data".
Step 4: Wait for the software to scan the SD card for the files stored on your SD card.
Step 5: Choose a file you want to preview and click the Preview button beneath the thumbnail to view its content.
Step 6: Tick the box before the files you wish to recover from the SD card and click the Recover button.
Please be reminded that you shouldn't restore the files to the affected SD card.
With all the files at hand, you can consider replacing a new SD card for later storage work.