The safest way to clean up /boot partition in Debian or Ubuntu

First check your kernel version, so you won’t delete the in-use kernel image, running:

uname -r

Now run this command for a list of installed kernels:

dpkg --list 'linux-image*'

and delete the kernels you don’t want/need anymore by running this:

sudo apt-get remove linux-image-VERSION

Replace VERSION with the version of the kernel you want to remove.

When you’re done removing the older kernels, you can run this to remove ever packages you won’t need anymore:

sudo apt-get autoremove

And finally you can run this to update grub kernel list:

sudo update-grub