Here's a link to a long article about vegan organic (veganic) gardening from The Vegan Society.

A little excerpt:
Vegan-organics is, briefly, any system of cultivation that avoids artificial chemicals and sprays, GMOs, livestock manures and animal remains from slaughterhouses or fish processing etc. Alternatively, fertility is maintained by vegetable composts, green manures, crop rotation, mulches, and any other method that is sustainable, ecologically viable and not dependent upon animal exploitation. This will ensure long-term fertility, and wholesome food for this and future generations.

Whilst conventional cultivation farming relies on synthetic chemicals and animal products, traditional organic production also generally relies on animal wastes and by-products. Both can be seen to have the exploitation of living creatures in common, with conventional agriculture also leading to terrible health, social, economic and environmental problems. Vegan-Organic methods involve none of these drawbacks. Many people who are not themselves vegan or vegetarian are coming to appreciate these benefits of animal free growing.