I am looking at purchasing a home that has the wire from the mast running into a 100 cut-off switch, then into a 60 amp panel. Would it be possible to change out the 60 amp panel to a 100 amp panel?

Maybe, maybe not. Older houses, say from the late 40's through the 50's, for the most part didn't have large electrical loads and used 60 amp panels. Without knowing the history who knows who or when the 100 amp disconnect was installed, or why a 100 amp disconnect then to a 60 amp panel. To upgrade to a 100 amp panel the service drop conductors, service entrance conductors, raceways (conduit), and the meter must all be sized accordingly. This is best left to a licensed electrician or the utility company to verify what you have and if you need to upgrade anything.

If it is #4 copper, you can, but, New Panel rated at 100+ will need to be installed in place of the 60. Don't know about aluminum.

What the important issue here is a 100 amp main protecting a 60 amp panel. If this is exactly true, then the serviced is a safety and code violation,and upgrading the panel to 100 amp is mandatory.

Before you purchase the home,have the service inspected thoroughly for any code violations, and have the seller incur any costs for corrective measures.

As explained so far, if the panel only can be changed depends on the wiring and equipment serving the panel. If it all rated 100 amps, then fine only the panel needs to be replaced.