You can't beat that with a stick is intended to be a humorous extension of
You can't beat that.
1.
To beat means to do better than (something, somebody), for example,
The runner beat the world record in the 1000-meter event.
2. To beat also means to strike repeatedly to inflict harm (with fists, a club, a stick), for example,
The gang ended up beating the man to death.
The "humor" is the combination of both meanings in one, taking the common idiom
You can't beat that (You can't do better than that) with the first meaning and extending it as if
beat had the second meaning.
The combination is not unique to this excerpt, by the way. It is
fairly frequently heard, but not as often as the plain idiom without
the extension.
Considering that this is said in the context of music, where a
conductor may "beat time" with a baton (also called a stick), there is
a rather clever third layer of associations here.
CJ