Rebbi — Rabbi Yehudah HaNasi — asked why the Torah specifically mentions "a rod" in the law about striking a bondservant. He argued that the word "rod" is extra — it is not needed for the basic legal ruling. Extra words in the Torah are never wasted. They serve as anchors for interpretive techniques.
In this case, the word "rod" appears in two separate legal contexts. It appears here, in the law of the bondservant, and it appears in (Leviticus 27:32), in the law of animal tithing: "All that passes under the rod." This shared word creates a gezeirah shavah — a verbal analogy that transfers legal principles between the two passages.
From the bondservant law, the Mekhilta derives a rule: the law applies to a bondservant owned by one person, but not to a bondservant jointly owned by two partners. The "rod" of the master implies a single master. Shared ownership creates a different legal category.
This same exclusion transfers to the tithing law through the gezeirah shavah. Just as a jointly-owned bondservant is excluded here, a jointly-owned animal is excluded from the tithe there. One word — "rod" — appearing in two different contexts, links two unrelated areas of law and applies the same exception to both. The Mekhilta treats the Torah's vocabulary as a web of connections, where a single shared term can bridge vast distances between legal categories.