First things first, make sure you have all your files backed up to a different device.
When installing Ubuntu,you'll be prompted to choose your installation type. Select "Something else".
This will take you to the Gparted partition editor.
You should see one or more NTFS partitions. That is (these are) your Windows partition(s). Then you should see an ext3 or ext4 partition. That will be where your LinuxMint is currently installed.
From your description you want to overwrite your Mint partition and add a separate /home partition.
To do this, Double click your Mint partition (/dev/sda5 in this example). This will allow you to edit the partition.
Resize this partition. Make sure it is at least 4GB. IN this example I chose 6GB. To figure how many MB you need, Multiply 1024 by the number of GB. (example: 1024 x 6GB = 6144MB)
Select Format partition. Later when you apply these settings All Data will be lost!!!
You'll want to set the mount point to
When you select "Continue" a Warning will pop up. Please understand that this will write to disk. And you could lose data on the edited partition.
This should leave you an new grey "Free space".
Double click on "Freespace", to "Create New Partition". In the dialog box that pops up select
ext4 and set the mount point as
Your final out come should look similar to this.
Continue with the installation.
For more information on using Gparted checkout dedoimedo.com