One article 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 might be a good alternative. Spartanism is a little more neutral to me than negative, but some folks might see it as slightly negative.
An article in the Atlantic - The Opposite of Hoarding discusses the challenges faced by folks with this specific flavor of compulsive disorder, because of the cultural view of 'decluttering' as a positive thing. It says "...there’s no official term for compulsive decluttering."