You can get rid of hostile mobs (slimes, creepers, skeletons, endermen, zombies, etc.) by setting your world to Peaceful mode via the options menu. As for animals (like sheep, cows, bats, etc.) you have to kill those manually or find a way to disable animal spawning using a command of some sort.
Newly Spawned: Baby. Out of the Water: Deep-Sea Diver. Tree Puncher: First Fight. Carpenter: Under The Carpet. StoneMiner:Newb. Coal Miner: Just Add Methane. Zombie Killer: Village Protector. Iron Miner: Burnt Hands.BudderGold Miner:Sky Army Stuck At Home: It's a nightmare Redstone Miner:Electrician.Diamond Miner: I'm rich! Lapis Lazuli Collector: Enchanting Time!