Minecraft Java Edition – Is It Possible to Get a Grass Block in a Dirt-Only World with Naturally Spawning Mobs?

With the silk touch enchantment on any tool, you can obtain a 'grass block' when digging instead of a dirt block. Place the grass in a patch of dirt and it will spread normally.

This is also helpful if you want to transplant Mycelium blocks.

Source: http://www.minecraftwiki.net/wiki/Enchanting

Passive mob spawning has changed in version 1.8. Animals now spawn when a new chunk is generated and they don't despawn. However, there seem to be some disagreement as to what happens if you kill all the animals around you. Some say that they don't respawn while others claim that they do but do so very slowly.

The best thread I've seen about this is this one posted mere hours ago. It seems to confirm what you see, that animals don't respawn at all. UPDATE: The same thread now seems to confirm that they do respawn, just very slowly.

Also, I think everyone agree that animals don't spawn in ocean biomes at all. I have played on a couple of islands far out to sea myself and have never seen animals there.

In version 1.9 breeding of animals will be introduced. Hopefully that will clear things up.