So, to test if your cell is blank, use:
=IF(A1="","Not Completed","Completed")
Easy enough, but you want the date instead of "Completed". So, our next step is to find where the date is within the cell.
If you have "Completed" and the date entered in a different order randomly, you will need to determine where to find "Completed" in the string the cell contains to determine the order. You can do that using:
=FIND("Completed",A1)
This will give you the starting position of the string "Completed" within "8/21 Completed" or "Completed 8/21". If this function returns 1, then the format is "Completed 8/21." Anything else and the format is "8/21 Completed".
Now, we just need chop up the string. If =FIND("Completed",A1) is equal to 1 then we want to use =RIGHT(A1,LEN(A1))-10. This will trim the string, starting from the right side, to whatever the length is minus ten characters (the length of "Completed "). If it is anything other than 1, we want to use =LEFT(A1,LEN(A1)-10). This will do the same thing but start from the left.
So, our full formula boils down to
=IF(A1="","Not Completed",IF(FIND("Completed",A1)=1,RIGHT(A1,LEN(A1))-10,LEFT(A1,LEN(A1)-10))