One [article][1] describes it as a mental illness: **obsessive-compulsive spartanism**. That's fairly negative, but you might not want the added baggage of diagnosing someone with a mental illness, so just [spartanism][2] might be a good alternative. Spartanism is a little more neutral to me than negative, but some folks might see it as slightly negative.


  [1]: http://www.wisegeek.org/what-is-the-opposite-of-hoarding.htm
  [2]: http://www.dictionary.com/browse/spartanism