will updating ios using mac mini will erase iphone data?

In theory it shouldn't if you only chose "update." An update even through the computer should just update the operating system and keep the data. The only reason it would erase the data is if you specifically selected an option for "erase" during the process.

+1 No it shouldn’t, but it is also a good idea to have the iPhone backed up to that Mac Mini or another Mac, just in case something should go south.