how to catch specific pyodbc error message

This worked for me.

    try:
        cnxn = pyodbc.connect(...)
    except pyodbc.Error as ex:
        sqlstate = ex.args[0]
        if sqlstate == '28000':
            print("LDAP Connection failed: check password")

There are different SQLSTATES and you can have if-else statements to print out the cause.

Similarly,

  try:
        cnxn = pyodbc.connect(...)
  except pyodbc.Error as ex:
        sqlstate = ex.args[1]
        print(sqlstate) 

will give you the second part of the error with description.
For exampleex.args[0] give you 28000 and ex.args[1] gives [28000] LDAP authentication failed for user 'user' (24) (SQLDriverConnect)

You can then use String manipulation techniques there to just print out what you want. Hope this helps.