Creative ways to deactivate alpha-amylase taken from fungi
Amylase inhibitors have attracted much attention because of their potential in treating type 2 diabetes. 

You can inactivate most enzymes by using a specific inhibitor. One class of inhibitors consists of molecules that resemble the substrate molecules but are not acted upon in the same way. These will bind to the active site and will prevent the substrate from binding. An inhibitor of many amylases is acarbose. This is a competitive inhibitor which means that inhibition is overcome by high concentrations of substrate.

And if that isn't enough to get you started here is an entire thesis on the topic of amylase inhibitors.

If you want to permanently block activity the ideal compound would be one which binds to and covalently modifies the active site, destroying enzyme activity. This would be an irreversible inhibitor. I haven't been able to find a reference to such a compound however.