Computer-use agents increasingly operate inside live personal workspaces, where their actions can modify files, applications, GUI state, credentials, and authenticated sessions. This creates a tension between safety and quality: agents need isolation and rollback to avoid damaging user state, but also need fast branching to support speculative execution and parallel search. Existing VMs, containers, and checkpoint/restore systems can isolate or recover workloads, but they do not provide low-latency versioning of a full interactive workspace. We present TClone, a forkable personal workspace system for computer-use agents. TClone enables a live GUI workspace to be snapshotted, forked into isolated branches, rolled back, and selectively committed or merged. Its design separates fast branch creation from durable checkpointing, using sibling containers, copy-on-write memory sharing, filesystem versioning, GUI-local execution, and asynchronous checkpointing. In our end-to-end agent-loop measurement, TClone reduces total task latency by 1.9x and 1.5x over KVM and CRIU. By making workspace versioning a first-class systems primitive, TClone supports safer and higher-quality agent execution over real personal computing environments.