Selecting the conversation header and pressing delete does not simply remove the current messages?
If not it appears MS only gives you two ways to clean/remove conversations, either using the clean up function, which removes duplicate info and keeps only unique information, or the ignore function, which sends all messages from that conversation, past, present, and future, into the trash (where they can be recovered later if you want).
Otherwise, you should be able to group as a conversation, highlight the desired messages, and then press Delete to remove the selected messages.
UPDATE for additional information from OP:
In an exhaustive search of all possible Outlook 2010 buttons/options, I did not find any options that correspond to what the OP wants. MS appears to have assumed that when using Conversation tools, the user will generally be in the Conversation view, in which case the solution would simply be to select the entire conversation and press the Delete key.
Absent using the Conversation view Outlook does not offer a function that will automatically delete all current messages in a Conversation without either using the "cleanup" function or the "ignore" function.
However, due to Outlook's extensibility, something like this shouldn't be too difficult to program as an add-in or plug-in for someone familiar with such programming.