In my view "say" is more normal while spoke or speak is more portentious. Certainly when you reading a book and it is describing what someone said, then the author will use "said" rather than "spoke".

I believe that the author of this article, if he was fluent, may have been trying to be creative with words for effect. However from the point of view of a language learner I would recommend disregarding this. The sentence as "don't say words that you don't mean" makes a lot more sense and sounds more fluent. 'say' tends to refer to the actual words so for example "you said the food was good here" or "don't say that, it's not very nice". 'spoke' more often refers to the act of speaking. For example "he spoke in Japanese" only tells you what he was doing not what he was saying or "Don't speak!" isn't telling a person not to say something specific such as not to be nasty but not to say anything at all. You may also find this table useful. https://staff.washington.edu/marynell/grammar/tellsay.html I hope this has helped.

With "speak to" there is a sense of addressing others in general whereas "say" is used to report or articulate specific words. e.g. The manager had to speak to his team about their poor performance. During this time, he said (to them) that they were not working hard enough. Consider using these structures: a) subject + speak + to + sb + about + theme b) subject + say [+ to + sb] + that + independent clause