Hi Lily_1 and welcome to the community!
Reformatting your new hard drive affects only it and not the internal drives as well. This means that if you start the reformatting process and if you have files on the WD Elements, you'll lose them and won't be able to access them anymore. However, everything on the internal drive of the computer/laptop should be intact.
I know you've mentioned that you know how to do it, but just in case, here's a tutorial on how to format a hard drive on Mac:
How to partition and format a WD drive on Windows and Mac OSX. Just click on the corresponding OS and follow the instructions.
Hope that helps.
Boogieman_WD