The cutter blades are ceramic and (allegedly) non-conducting. There are two pyrotechnic pistons, basically the same principle by which automotive airbags are deployed. Both are activated along redundant firing circuits and only one has to fire in order to activate the blade.
For many aircraft and spacecraft applications in the 1950s up through the 1970s, you'd use terminal blocks. But wiring those up correctly is error-prone (e.g., Apollo 6 second stage) and requires skill. Then you have the Bendix connector, which is far less error-prone since it's just a keyed connector, but its mechanical strength is lengendary. Any other kind of connector that pulls loose simply upon extraction force is bound to shake loose upon launch. And with any pin-in-socket type connector, bent pins during assembly is a chronic problem requiring reworking the whole harness.
Yes, mechanical relays were used in electrical deadfacing. And no, they're not especially robust items. However there are special deadfacing relays that are useful only for that purpose. With most relays, there's a spring-loaded armature that is held in one position by the spring and moved to the other position by a control force, typically an electromagnet. They fail in space environment for any number of reasons, typically by contamination that prevents the armature from operating or by failure of the spring. In a deadfacing relay there is no "must continue to act" force holding the circuit closed, so it operates in failsafe mode until the control force acts. The relay mechanism is simpler and less prone to contamination, and assembled under clean-room conditions then sealed. They achieve higher-than-usual reliability.
