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I think OP specifically asked for a way that did not involve duplicating and scaling.
The Maya API has some options, in a nutshell:
import cmdx
# Read original points
original = cmdx.selection()[0]
original_points = [p.read() for p in original["controlPoints"]]
# Negate an axis
negated_points = [(p[0], p[1], p[2] * -1) for p in original_points]
# Make new curve
parent = cmdx.createNode("transform", name="negated")
curve = cmdx.curve(parent, points=negated_points)
Key parts being the curve
function, which is here and iterating over the controlPoints
array attribute which you can do using cmds too.
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