Residential tree removal is pretty darned expensive, and I don't have any tips for getting rid of trees for cheap or free. But I can share how we reduced our cost, and gained value from unwanted trees
When we bought the tea room, it came with a large yard full of grass, black walnut trees, scraggly, stinky, over-grown cedar trees. The cedar trees covered the front of the house, and the walnuts lobbed green grenades into the yard in the fall (I spent 6 months walking with a limp after I rolled my ankle on a black walnut). They had to go.
Because some of the trees we were removing were large black walnuts, we were able to recoup part of the cost by selling the logs to a local sawmill. The branches that were too small to mill were given to a family who needed firewood to heat their home for the winter. Making mulch out of black walnut trees is a very bad idea, so we chose not to go that route.
We brought the cedar logs home to our farm. We plan to have them milled into lumber to build some raised beds. Some day.
We tried using a small wood chipper to turn some of the smallest cedar branches into mulch. I'm not sure I can say that last is a frugal way to go, however. A small wood chipper still costs over $300 new, and it takes for-ev-er to shred even the smallest branches. We did wind up with a nice pile of cedar mulch to spread around the foundation of the tea room. I'd like to think it helps repel insects, but at the very least, cedar mulch smells much better than live cedar trees!
In the end, having 3 black walnut trees and 3 cedar trees cut down and the stumps ground cost us around $3,500. The walnut logs sold for around $2,000. My very rough guess is that the cedar mulch we generated would have cost us in the neighborhood of $100-$200 from a big box store. I have never purchased firewood in my life (we cut our own from trees that were logged off our farm), so I have no idea how much those smaller branches were worth as firewood.
$1,500 out of pocket is still a lot of money for most people, but it is significantly less than $3,500.