The diploma is basically extra subjects that allow you to gain a secondary qualification alongside your main degree; if I took a Diploma of Mathematics alongside my Zoology major I would graduate with a BSc (Zoology) and the diploma qualification in mathematics. If you're already doing a major in a mathematics field and don't want to do a non-mathematics major in your degree, the diploma is probably not very useful to you; you can't take the diploma in a maths field if your main major is already focused on one of the mathematics fields.
What you CAN do is credit maths subjects you've already done (up to four) to the diploma and then complete a major in something else such as Physics, Marine Biology, Geography or whatever your particular subject selections and interests lead you to do, while completing another four-ish maths subjects (you need eight in total for diploma completion) in your diploma. As a result, you come away with two qualifications rather than one. In your instance you would need to assure the university that your science major wasn't planned as mathematics, but rather engineering, to be accepted into the diploma (since they don't let maths majors take the course).