Is all data used with OpenClaw saved locally

No - OpenClaw’s state is local, but external services still see what you send them.
Local by default: sessions, memory files, config, and workspace live on the Gateway host (~/.openclaw + your workspace directory).
Remote by necessity: messages you send to model providers (Anthropic/OpenAI/etc.) go to their APIs, and chat platforms (WhatsApp/Telegram/Slack/etc.) store message data on their servers.
You control the footprint: using local models keeps prompts on your machine, but channel traffic still goes through the channel’s servers.
Related: Agent workspace, Memory.