Before you install your new distro you may want to back up all of your files. I do--
If you haven't already you may want to check the size of your Win's parttion. It may be that you will have to shrink the Win's
partition first before proceeding with the Linux Mint Debain install. Unless; of course you already did that-
The Linux Mint Debian distribution that you want to install; should; during the installation process include a 'partition manager'
to allow you to delete the 'Ubuntu' partition. This is most likely the 'manual' or 'expert' option.
With some distributions (Fedora)
the installer automatically installs/configures the partitions of the distro for you.
Once you delete that Ubuntu partition you can use the free space to 'create a new partition' for your Linux Mint Debian distribution.
When you create the new partition your should choose to make it a "ext4" journaling file system.
And than make another partition for your Linux 'swap' 1 GB should be sufficient 2 GB may be overkill-
During the Linux Mint Debian installation Grub, the bootloader should already be configured for you and you should see a message during the
install that says something like: 'Configuring the bootloader'
In order to view the partitions on your computer; if you could, post the output of this command:as 'root'
It shows all of the partitions in a readable table.
Is this a Desktop or a laptop?