Some Windows apps can be used under WINE (http://www.winehq.org
) on Linux, but not all, and not always with perfect compatibility. You should go to the WINE site and see what they say about specific versions of specific Windows apps. You don't even need a valid copy of Windows to run programs under WINE, because you're not technically running Windows, just a program that can install and run (some) Windows apps.
Another option is to dual-boot your machine--that is, leave your Windows install on there but shrink its partition and install Mint on new partitions in the freed-up space. You can even make a dedicated data partition (preferably partitioned as NTFS) that can be accessed from either the Linux side or the Windows side. This works fine for me, though I'm no expert. You could start by using Mint for your day-to-day stuff (e.g., Web browsing, word processing) and boot into Windows for your work. Then, you can gradually start looking into whether you can start shifting more and more of your work from Windows onto Mint. This way you don't have to make the switch all at once.
The third option I hear about, though I've never done it, is to install Linux and then use VirtualBox or something similar to create a "virtual machine" within the Linux install, into which you then install Windows and your Windows applications. You do need a valid copy of Windows for this, because you are actually running Windows ... just on a virtual machine rather than a "regular" one.
There are tutorials for all these things, if you decide you want to explore these options.
Olivia 15 Cinnamon 64, dual-boot Win 7 Pro 64 SP1, Clevo W150ER 15.6" laptop, i7 3630M, 16 GB RAM, Samsung SSD 840 Pro 256 GB/HGST 1 TB 7200 RPM, Nvidia GT 650M 1 GB, USB 3.0 HGST 1 TB 7200 RPM, HP Photosmart C5280