#1 DYOD, Do Your Own Demo!
Who doesn't love swinging a sledgehammer and breaking stuff?! This is a fun and achievable way to save some money on a project. You may be wise to consult with your contractor prior to doing so to ensure you don't take out too much, or encounter any unexpected surprises. There could always be electrical, plumbing, etc. considerations when doing demo. And always be aware that you could encounter surprises once you tear into a wall or floor, etc. This is a common issue with remodeling, the hidden surprises that you just don't know are there until you peel the cover away.
Painting can be a lot of work, but if you have the time and energy, this is a great way to potentially save thousands in your project budget. In general, painting is not that technical. However, there can be obvious hazards and more technical problems which may warrant the seeking of a professional's help.
Who doesn't love being outside and getting some much needed nature therapy?! Although this wouldn't apply to all projects, if it is a part of yours you could save a lot of money by designing and building your own landscaping.
Of course, as with any task, some require the tools and expertise of a professional. And, you should always consult and coordinate with your contractor to ensure that it makes sense for your project that you perform some of the tasks.
Any questions? Don't hesitate to ask!