table selectrows looking for more than one thing

You need to repeat the entire test  (Text.Contains)

and you need to connect the tests with an or , not an and

I also suggest you make the test case-insensitive

= Table.SelectRows(#"Exclude Blank and NA Notes", each 
                 Text.Contains([Notes], "No note from tutor", Comparer.OrdinalIgnoreCase) 
              or Text.Contains([Notes], "No notes from tutor",Comparer.OrdinalIgnoreCase))

You could also use the List.Contains method as suggested by jgeddes  but, again, I would add the case insensitive option:

= Table.SelectRows(#"Exclude Blank and NA Notes", each 
            List.Contains({"No note from tutor","No notes from tutor"},
            [Notes],
            Comparer.OrdinalIgnoreCase))