Activate coin control features in Bitcoin Core to select exactly which inputs to use for each transaction. It's up to you to use a different address for each transaction, most wallets do that by default.

The whole concept of a blockchain means you can see exactly where any transaction came from. If you don't want that, but still want to use Bitcoin, you'll have to use a mixer.
Is there any specific reason you want the receiving party not to see where it came from? It's easier to give the right advice if you explain why you want this.