General synonyms:
* Compostable
* Decomposable
* Disintegrable
* Degradable
* Biodeteriorable
* Naturally decomposing
* Environmentally friendly (in the context of breaking down)
More specific synonyms:
* Bioresorbable (for materials that break down in the body)
* Photodegradable (for materials that break down with sunlight)
* Hydrodegradable (for materials that break down with water)
The best synonym depends on the specific situation and what you want to emphasize.