LabVIEW for Linux is not downloadable like the Windows version is. In order to get it, you must purchase it and then wait for the CD. You can order your copy here: http://sine.ni.com/nips/cds/view/p/lang/en/nid/2541
National Instruments only officially support LabVIEW for Linux on Scientific Linux, Red Hat Enterprise and OpenSUSE. For more on which versions check here:
http://www.ni.com/pdf/manuals/375845a.pdf
It may be possible to install LabVIEW on Mint, but you will probably have to do some digging and also some trial and error.
I understand there are different Mint projects and that they are based on different distros. Which Mint are you using?