Privacy concerns in smart contracts have led to systems that protect on-chain data but still rely on trusted off-chain parties. We propose a novel framework for doubly private execution that addresses both on-chain and off-chain privacy, allowing clients to submit requests confidentially to potentially untrusting servers that collaboratively process these requests without learning client identities or data. Our implementation, Jigsaw, extends the ZEXE architecture and Collaborative zkSNARKs to enable efficient proof generation by server groups. Jigsaw introduces a novel collaborative zkSNARK construction with low latency and reduced proving time, demonstrating 40-50x faster proof generation and orders-of-magnitude less bandwidth than naive approaches when tested on applications like decentralized exchanges, auctions, and voting.