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Like this maybe ?

sage: Q = QuadraticForm(ZZ, 3, [1,2,3,4,5,6])
sage: Cl = CliffordAlgebra(Q)
sage: D = Cl.tensor_square()
sage: D in Algebras(ZZ)
True
sage: D.one()**2
1 # 1

Like this maybe ?

sage: Q = QuadraticForm(ZZ, 3, [1,2,3,4,5,6])
sage: Cl = CliffordAlgebra(Q)
sage: D = Cl.tensor_square()
sage: D in Algebras(ZZ)
True
sage: D.one()**2
1 # 1

EDIT: I missed the point that you wanted some other product. You may look at the doc of tensor_square.