Para deletar mensagens através do POP3, basta seguir o exemplo abaixo:

<%
Set pop3 = Server.CreateObject("Chili.Pop3.1")
pop3.Connect "mail.server.com","use@domain.com","****"
on error resume next
for each item in pop3.Messages
indice = indice + 1
Response.Write "To: " & item.to & "<BR>"
Response.Write "From: " & item.from & "<BR>"
Response.Write "Subj: " & item.subject & "<BR>"
Response.Write "Msg: " & item.message & "<BR>"
Response.Write "Msg: " & item.MsgId & "<HR>"
next
pop3.Delete indice-1
'pop3.Reset
pop3.Disconnect
%>