Welcome slc0904,
Thank you for using Apple Support Communities. Based on your post, the Mail app is stuck importing emails on your Mac. We'll do our best to assist with this.
There wouldn't be a way to avoid the import process. You'd want to give the Apple Mail app time to complete the import. We'd recommend leaving the Mac on, connected to a network, with the Mail app open to complete the process.
With that said, should the issue persist, have you recently restored the Mac from a backup or migrated from another computer? What happens if you test safe mode? Here's how to boot there to test it out: How to use safe mode on your Mac Safe mode is a good way to isolate the behavior further, as it can prevent some apps and processes from running while booted there.
Hoping to hear back, take care.