How do I deal with sending low GPA to a potential supervisor? A professor offered to meet with me later this week to discuss some potential projects, and asked for my transcripts to see what courses I have taken and how well I am at them. 

I have done decently in my mathematics courses, however, one semester last year was exceptionally bad for me and I ended up getting a C-, C+ and a D- (in discrete math, Introduction to C, and a biology course respectively). The only course that has some sort of relation to the research I'm interested in doing is the intro to C course. 

I honestly don't know how to proceed with this. I don't want to keep making excuses for myself because I'm not doing incredibly well in my professor's class, but I know I can get better at the software being used (MATLAB), as I've used it before for maths classes and haven't had much trouble with it. I know he thinks I'm not the best programmer and I don't know how to deal with that idea and this situation.  

How do professors deal with this? I don't want to waste his time, and more importantly, I don't want to become disinterested in the project and end up giving up halfway.
I wish I had a better answer for you, but the only thing that can fix a semester like that is more recent semesters with better grades, and the more of them the better.

Irrespective of the current situation, I think what you need is to focus on getting several solid semesters between you and this rough one.  Then when someone who is interested in your academic performance asks, you can show them that, yes, you had a rough semester, but you've gotten back on track.  In my experience, recent good performance will very quickly outweigh more distant struggles.  This is true regardless of the reason - you could have the best excuse in the world, but if you haven't shown you're past it and doing better now, who's to say you won't continue to struggle with whatever you're being considered for?

Given that your rough term was just last year, however, the only recourse you have right now is to be open and upfront about it; explain why you struggled and what happened to address the cause.  If you have no excuse, then just say that too.  It was a rough term, but you're back on track.  This is totally reasonable and far from uncommon in undergrad.  Unfortunately it may be a hard sell if you're currently struggling in this professor's class too.  Do you know why the professor made this offer to you in spite of this?  That might offer some insight into what they're looking for.

In short, send the transcripts, point out that you struggled but mention what you did to address the cause, and then the ball is in their court.  Be prepared for the possibility that the professor is alarmed by what they see, and know that it may take time for you to build up this kind of credibility again.  Then focus on your grades.

Good luck!