Consider the half reactions:
\begin{align} \ce{Na^+ + e- &-> Na} &\quad E^\circ &= -\pu{2.71 V} \tag{1}\\ \ce{Cu^2+ + 2 e- &-> Cu} &\quad E^\circ &= \pu{+0.34 V} \tag{2} \end{align}
Can I say that $\ce{Na+}$ is more stable than $\ce{Na}$ since $\ce{Na+}$ has negative potential? If so, can I also say that $\ce{Cu^2+}$ is less stable than $\ce{Cu}$ so $\ce{Cu^2+}$ has a positive potential?
Remember that reduction potentials do not have any meaning by themselves. They are measured against a hydrogen cell to which arbitrarily we assign the value $E^\circ=0$. You can compare between different potentials. For example, in your case, you could say that that $\ce{Cu^2+}$ has a greater tendency to be reduced than $\ce{Na^+}$ because its reduction potential is more positive. However, I do not think the potential itself tells you anything with regard to the stability (and, in any case, what do you mean by that) of the species involved in a particular half reaction.
