If you haven't cleared the apt cache (by doing a sudo apt-get clean, for
instance) then the downloaded package debs are stored in
/var/cache/apt/archive (on 10.04, at least). You should be able to copy
them over and run them on your Mint system, but be aware that there may
be unsatisfied dependencies which could cause problems.

If, however, you have cleared the cache, then this is going to prove
very problematic as the package will have installed its files all over
the place. You can go into Synaptic, right click on an installed
package and, under properties, get a list of all the installed files and
where they were installed. You could use this information to transfer
the package over, but I wouldn't recommend it unless you're a true
masochist.