My pipe is cracked or collapsed. Does the garden have to be dug up?

Not always. There are two broad approaches:

No-dig relining (CIPP). A resin-based liner is inserted into the existing pipe and set in place, forming a new pipe wall inside the old one. This seals cracks, blocks root entry, and adds strength, with only a minor reduction in diameter that is offset by smoother flow. It avoids excavation.
Patch repair. A localised liner repairs a single damaged section rather than the whole run.
Excavation. Where a pipe has fully collapsed or relining is not possible, the affected section is dug up and replaced.

Relining is faster and less disruptive than excavation and is suitable for many cracked or leaking pipes. The right method depends on the extent and type of damage, which a CCTV survey establishes first.