"1111A" is the value
In python for example
>>> a = "1111A"
>>> b = a[:-1]
so in the field calculator, you would setup a new field probably text if you can't guarantee all the slicing will be numeric, then use the field calculator syntax with the python parser selected a
the : means everything up to and -1 means the last one (counting backward from the end. There is a whole section on field calculations in the online help files... ie from the 10.3 help Fundamentals of field calculations—Help | ArcGIS for Desktop