Does the Word Substract Exist?

Though the obsolete word "substract" did exist, any occurrence you see these days is most likely just a common mistake, formed by analogy either with "abstract" or with other languages whose corresponding words do have two 's's.

Which one is correct subtract or substract?

Subtract is considered the only correct verb, while substract is considered wrong or at least "very" obsolete.

Why do people say substract instead of subtract?

Long story short, the correct forms are “subtract” and “subtraction” (without “s”). The reason why so many English learners make the mistake is probably that there is a corresponding word in many languages that does contain an “s”, e.g. soustraire in French or sustraer in Spanish.