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We prove that in the Cayley graph of any braid group modulo its center$B_n/Z(B_n)$, equipped with Garside's generating set, the axes of allpseudo-Anosov braids are strongly contracting. More generally, we consider aGarside group $G$ of finite type with cyclic center. We prove that in theCayley graph of $G/Z(G)$, equipped with the Garside generators, the axis of anyMorse element is strongly contracting. As a consequence, we prove that Morseelements act loxodromically on the additional length graph of $G$.

Morse elements in Garside groups are strongly contracting