Can an iMac 27' mid 2010 be used as a monitor for the new Mac Mini M1

Connect it to one of the Mac mini's USB-C ports with:

mophie USB-C Cable with Mini DisplayPort Connector - Apple

Use your iMac as a display with target display mode - Apple Support

( The "Mac from 2019 or earlier" is for Thunderbolt connection, and doesn't apply for your Mini DisplayPort 2010 iMac.)

Have you unmuted the sound, and raised the volume using the iMac's keyboard?

Before entering Target Disk Mode, check the iMacs Sound preference. Check the Output settings.