Step 1: State the definition.
A transition metal is an element whose atom or one of its common ions has a partly filled d-subshell. If both the atom and its usual ion have a completely filled (\(d^{10}\)) or empty d-subshell, it is not a transition metal.
Step 2: Check each option's electron arrangement.
Sc: \([Ar]3d^1 4s^2\), and \(Sc^{3+}\) has \(3d^0\) but the atom has partly filled d, so it is a transition metal. Cu: \([Ar]3d^{10}4s^1\), and \(Cu^{2+}\) is \(3d^9\) (partly filled), so it is a transition metal. Ag: \([Kr]4d^{10}5s^1\), and \(Ag^{2+}\)/\(Ag^+\) common ion behaviour still allows partly filled d in some ions, and Ag is grouped as a transition metal.
Step 3: Examine Hg.
Mercury has the configuration \([Xe]4f^{14}5d^{10}6s^2\). Its common ion \(Hg^{2+}\) is \(5d^{10}\), which is completely filled.
Step 4: Apply the rule to Hg.
Since both Hg atom and its \(Hg^{2+}\) ion have a fully filled d-subshell, Hg does not meet the condition for a transition metal.
Step 5: Conclude.
The element that is not a transition metal is mercury.
\[ \boxed{\text{Hg}} \]