As Ubuntu is based on Debian, and Linux mint is made from Ubuntu, the software with Debian (.deb extension), will work on both.
Here is how..
Download the software with .deb extension.
For eg: wordpress.com-linux-deb-6.14.0.deb
Copy the file to your Downloads folder.
Open your terminal (Ctrl + Alt + T)
Type the following code
Now your Downloads folder will be opened in Terminal.
Note: If your downloads folder is named as “Downloads” and you type, “cd downloads” will not work. It should be strictly “cd Downloads” with capital “D”.
By default, the downloads folder is named as “Downloads”.
Now its time to execute or run the debian package in the Downloads folder.
Type the following code.
sudo dpkg -i [TYPE YOUR FILE NAME]
For eg: sudo dpkg -i wordpress.com-linux-deb-6.14.0.deb
Now your file will be installed.
Note: You should type the right file name in the code. You may copy paste the file name with extension to the terminal.
Close the terminal, after the installation is finished.