Mechanical methods and extreme chemistry aside, there is no instant method of dissolving bulky calcium sulfate (or its hydrates: $\ce{CaSO4 · 0.5 H2O}$ and gypsum $\ce{CaSO4 · 2H2O}$).
Soda-acid treatment
Since $\ce{CaSO4}$ is notably one of the reasons for permanent water hardness, industrial scale machinery using water heat exchangers or boilers are typically liberated from calcium sulfate by washing the insides with concentrated hot sodium carbonate solution for several hours, converting sulfate to less soluble carbonate, which is subsequently dissolved in inhibited acid solution (the process might take half a day or longer):
$$
\begin{align}
\ce{CaSO4(s) + Na2CO3(aq) &<=>> CaCO3(s) + Na2SO4(aq)}\\
\ce{CaCO3(s) + HCl(aq) &-> CaCl2(aq) + H2O(l) + CO2(g)}
\end{align}
$$
Complexing
There are numerous commercially available mixes for cleaning molds used for gypsum casting within hours.
Exact composition is usually classified as a trade secret; the majority of the manufacturers would list two main components:
- Alkaline cleansing agents. To put it simply, any alkali, e.g. $\ce{NaOH}$.
- Complexing agents. Most likely, these are disodium edetate $\ce{Na2H2EDTA}$ and sodium citrate $\ce{Na3C6H5O7}$.
The idea behind using EDTA salts is pretty simple: it makes insoluble metal salts soluble by making chelate complexes such as $\ce{CaNa2EDTA}$ which are stable (and well-soluble) in water.
Citrate may also complexate calcium, and alkaline medium promotes complex formation.
This method is widely used in analytical chemistry for the qualitative and quantitative determination of numerous cations (transition and rare-earth metals, actinoids).
Both of the above-mentioned methods may be significantly accelerated if the diffusion barrier is lowered, e.g. by using ultrasonic bath.