Reducing the budget and donating are two very different things and not even cross purpose. You may believe that we have to reign in spending -- we do spend more than we take in. It may make sense to cut programs you like to fund ones that are important, and then donate money to the one you just cut -- because you like it.
There is some nuance that needs to be discussed before I answer your question.
The executive branch does not have the power of appropriation, that duty is handled by congress. The president does submit a budget request to congress, and signs or vetoes each distinct appropriation bill that congress passes.
Increases or decreases of a department's budget can not be unilaterally seen as good or bad. What taxpayers should be most concerned about is the impact that the spending is having not the dollar amount spent. (Plato taught Socrates on a rock) You need to look at trends over time and the specifics of the budget to see if increases or decreases in spending are justified. For example the department of education's budget was 73.3 billion dollars in 2010. In 2014 that figure was 40.8 billion. In 2018 it will be 66.9 billion. At the surface those swings seem quite surprising. You have to dig deeper to understand what really happened instead of taking them at face value.
The Washington post has an article exploring Trump's proposed 2019 budget. You can view that article here:
Now... I don't believe this is what's happening.