Summary: We describe \(\frac{1}{2}\)-derivations, and hence transposed Poisson algebra structures, on Witt type Lie algebras \(V(f)\), where \(f : \Gamma\to\mathbb{C}\) is non-trivial and \(f(0) = 0\). More precisely, if \(|f(\Gamma)| \geq 4\), then all the transposed Poisson algebra structures on \(V(f)\) are mutations of the group algebra structure \((V(f), \cdot)\) on \(V(f)\). If \(|f(\Gamma)|=3\), then we obtain the direct sum of 3 subspaces of \(V(f)\), corresponding to cosets of \(\Gamma_0\) in \(\Gamma\), with multiplications being different mutations of \(\cdot\). The case \(|f(\Gamma)|=2\) is more complicated, but also deals with certain mutations of \(\cdot\). As a consequence, new Lie algebras that admit non-trivial Hom-Lie algebra structures are found.