Where is that partition mounted? At the root? If so, start with that command to remove the .deb packages (not the installed programs):
$ sudo apt-get clean

Then, remove the older kernels. From the Synaptic package manager for instance (assuming 'sudo apt-get clean' was enough to make it properly work), you can search for the installed packages named "linux-" followed by a string including some version number ("3.13.0-45" for instance) and remove all those not having the highest version number.

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