Everytime I learn Mathematics, I do it the slow-way.
Slow is not good. But superficial is worse.
I tends to read the definitions until I make sense of what is written in the texts.
I wish every student did this. Fantastic, well done, don't stop doing this, ever.
Do, however, consider using alternate sources—multiple alternate sources—to look up key definitions. Think for yourself, and ensure that what you are reading makes sense to you.
The test of any “truth” is whether it is true for you. If, when one has gotten the body of data, cleared up any misunderstood words in it and looked over the scene, it still doesn’t seem true, then it isn’t true so far as you are concerned. Reject it. And, if you like, carry it further and conclude what the truth is for you. After all, you are the one who is going to have to use it or not use it, think with it or not think with it.
—The Way to Happiness, section 17-2, "Learn"
(The above linked article is highly recommended reading, by the way.)
I can spend a whole day trying to get one page of the textbook.
To be frank—to me, this means your textbook is probably badly written. Sorry.
(Or, it means you're studying at the wrong level. A middle school student given a well-written college math text would spend a long time on each page, too.)
I also do all the theorem proving by myself, even it takes me a lot of time to do that.
Good. Keep doing this. There is no better way to learn math than by actually understanding and working through the concepts yourself.
You may want to start differentiating the important theorems from the unimportant. Start considering which theorems will expand your knowledge and understanding of math, or even just which theorems you are interested in. Which of the theorems have application or relevance to the understandings of math you already have?
It's not necessary that you perfectly understand every theorem you ever read...and even if you do want to attain that, you may attain it more rapidly with important theorems and proof techniques under your belt.
The works tend to take a longer time than everybody else, but I do get the feeling I know the material better than other guys in my class.
You're probably correct on both counts.
My advice to you:
First, the article I've linked above contains some excellent tips on learning in general, not limited only to mathematics. Start with that. (You can turn off sound if you like, but the one-minute video is actually pretty cool.)
Then, from my own experience in studying mathematics, I will add some specific points:
Ensure you get clear, accurate and precise definitions for every mathematical term used in your text. (And every other term, too, for that matter.)
If you have to fumble around mentally to remember what five of the words used in the sentence mean, you're not likely to catch the meaning of the sentence.
The same goes for notation. Play with newly introduced notation until it is as clear to you as English, or maybe even clearer. The notation itself must not be a barrier to your understanding. Play with it, and practice, practice, practice.
You're learning a language. Learn it well.
The ideas you are studying must become thoroughly familiar, common ground to you. You need to drill on the basics of the branch of math you are studying until you know them cold.
You haven't mentioned any specific branches of mathematics, so I will mention a couple examples myself from my experience as a high school math teacher:
Trigonometry students start flying after they are drilled and drilled and drilled and drilled on a simple right triangle diagram with a letter for each acute angle and a letter for each side.
"What's sine x?" "Uh, P over Q." "Good. What's arctan F over P?" "Uh, angle c." On and on and on (ensuring you wait for the correct answer each time no matter how long it takes, and then validate the correct answer when given) until the student gets every question correct without appreciable hesitation.
With several right triangles of different sizes drawn in random orientations, and with all different letters, this makes an excellent drill.
(Actually it's several drills, all with the same setup of several triangles. First, just do sines of angles. Then cosines of angles. Then tangents. Then randomly alternate between sin, cos, tan. Then cover cotangents. Then secants. Then cosecants. Then randomly between all six basic functions. Then start into the inverse functions: arcsine, arccos, etc. Always back it up if the student has trouble and make sure you allow the student to succeed; he should win at the drill.)
There is a similar set of drills for Calculus. (Gosh, I should probably write these up in a book....)
The point is that you need to get the basics of the branch of math perfectly understood without the slightest hesitation, so you can read fluently whatever is expressed about that branch of math.
One of the most thorough students I ever taught had this as his only shortcoming: He got everything 100%, but he didn't work toward fluency, so he remained slow. He didn't see $8!/6!$ and think instantly, "(seven times eight equals) 56" too fast to even think the words.
The only other advice I have, is work everything out on paper or better yet, in your head. If you are using a calculator or computer to "avoid errors," you shouldn't be using a calculator or a computer yet.
Once you are 100% confident in your ability to compute the answers yourself, with pencil and paper, and are solely using a computer to save time—then, okay.
But, if you really know your stuff, the absence of a computer or a calculator won't bother you much. It hardly saves any time at all, if you get sufficiently fast and well-practiced.