Can I upgrade my Mac Mini (mid 2011) from a macOS High Sierra V 10.13.6 to the latest version of macOS Big Sur?

Nope. High Sierra seems as far as it will upgrade. It isn't on the Mojave compatible list, either.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:

• MacBook (Early 2015 or newer)
• MacBook Air (Mid 2012 or newer)
• MacBook Pro (Mid 2012 or newer)
• Mac mini (Late 2012 or newer)
• iMac (Late 2012 or newer)
• iMac Pro (2017)
• Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)

macOS Big Sur is compatible with these computers:

MacBook introduced in 2015 or later

MacBook Air introduced in 2013 or later

MacBook Pro introduced in late 2013 or later

Mac mini introduced in 2014 or later

iMac introduced in 2014 or later

iMac Pro

Mac Pro introduced in 2013 or later

View the complete list of compatible computers.