I think it would be helpful to know why you are deleting the information from the source table as well as what kind of table it is(stage, etl, dim, etc..). It wouldn't help either if you specified whether you want to delete the table itself or just data in the table.
Since you specifically said "also delete the data in the source table" I will take it that you would like to keep the table itself. In which case if you add an 'Execute SQL task' and inside of that task you put a T-SQL statment to truncate the data in the source table you will delete the information source table data.
Now remember to add that Task after you have inserted into the destination table itself considering you referenced how you would like to delete source data after the move. below is T-SQL code to truncate and if you are not sure what truncate does look up the function on MSDN for reference(but essentially it deletes table data while keeping the table and the structure itself in place).
TRUNCATE TABLE schema.tablename
if you would like to delete the entire table the code below should work as well
DROP TABLE schema.tablename
Also this solution is only applicable if you are copying all the information from the entire source table to a destination table if you are taking only small specified sections such as only a couple columns or rows that you have identified then you will need to do the same identifications to remove those rows.
in which case you should look up documentation on DELETE and possibly CURSOR for use in deleting specific rows.