The default is to delete the entire conversation. If you're hitting the big "Delete" button near the top of the page then that's what is happening.
However, it is possible to delete individual messages from a conversation. While viewing the conversation you need to open the menu for the individual message. (It's the down arrow next to the reply button.) From there you can delete an individual message from a conversation.
As you mention, that's going to be labor-intensive. You're probably better off turning off conversation view altogether if you're going to be doing this regularly (as mhoran suggestsas mhoran suggests).