Moderators can delete content as well.
To answer your question, I'll go ahead and assume that you are asking the following:
Is there a way to give a user the ability to delete content that was created by other users, a blog, as an example, without giving them full admin rights?
It is absolutely possible to give users this ability without giving them full admin rights. The first question you will want to ask is: Where do I want this user to have these permissions? As noted here, Core Help , permissions are different depending on the place you assign them. One way to provide those permissions within a particular space is to assign the user the standard space permission level of Moderate. Another way would be to create a custom override for that user which provides them with Moderate Content permissions. For more information on these options, please review the following sections of the Jive Documentation: