Welcome to SolidWorks forums Peter.
I've no idea on how things work on MAC but make sure that your OS is 64 bit also as DraftSight is unsupported on Mac 32bit machines. You may get more information here: DraftSight SwYm community
Also I don't think that removing DS apps from your machine will destroy/remove/delete the drawings. If you still feel like that then create a back of all the drawing files in your machine before removing the app.
You might also find this post helpful for your future reference.
I am having exactly the same problem. Draftsight (V1R4.0) used to work on my Imac running OS X 10.6.8 64 bit.
I formatted and restored the machine's OS X 10.7.5 (64 bit). Draftsight asked me to activate, I filled in all the fields and received the activation link, and the confirmation after clicking it. But now whenever I launch Draftsight, it throws "This product is not licensed or has expired" and quits.
Any ideas on how to solve this?
Thanks in advance...
Really draft sight same issue 64 bit macbook pro running OS X 10.9.1 installed draft sight beta V1R5
keeps now asking for activation - got to get this act together folks - I want recomend buying this for our company I cannot do that when it like this.