There are two little clues you can use.
First, mercury(I) isn’t actually present as $\ce{Hg+}$; the cationic species is actually $\ce{Hg2^2+}$ with a $\ce{Hg-Hg}$ bond. Thus, if this were a mercury(I) compound, the sum formula would be $\ce{Hg2[Co(SCN)4]2}$.
This obviously only helps you if the correct formula was supplied as part of the question but the second clue is independent:
Look up a table of standard electrode potentials. There are two redox reactions that can occur, they are reproduced below:
$$\begin{align}
\ce{2 Hg^2+ + 2 e- &<=> Hg2^2+}&&&E^0 = \pu{+0.91V}\\[1.0em]
\ce{Co^3+ + e- &<=> Co^2+}&&&E^0=\pu{+1.82V}\\
\end{align}$$
The half-cell with a higher standard electrode potential will oxidise a half-cell with a lower standard electrode potential which means that, in solution, cobalt(III) and mercury(I) should react as follows:
$$\ce{2Co^3+ + Hg2^2+ -> 2Co^2+ + 2 Hg^2+}$$
As
$$E^0_\text{cell} = E^0_\text{red} - E^0_\text{ox}$$
we get a standard cell potential of
$$E^0_\text{cell} = \pu{+1.82V} - (\pu{+0.91V}) = \pu{+0.91V}$$
which is clearly positive, indicating a spontaneous reaction.
Of course, this is using aquacomplexes of both cations rather than whatever structure they would have in the complex you are supposed to name. Different chemical environments will modify a reaction’s electrode potential. However note that the uncorrected potential difference is so large – $\pu{+0.91V}$ – that it will be very hard to stabilise these otherwise incompatible oxidation states in solution.
On the other hand, a compound made up of mercury(II) and cobalt(II) is redox-stable.