You could say "My wife has ten bags made from leather", but " ... made of leather" sounds more natural to a native speaker of English. KhaledRa's phrase would make sense if "leather" were a proper noun (and therefore capitalized). If "Leather" is a place or a person, then bags can be from that place (identifying the origin) or person (indicating that they were a gift).
Die Tüte is a bag made either of paper or plastic to pack your shopping: Papiertüten, Plastiktüten. https://www.duden.de/rechtschreibung/Tuete
Die Tasche is either a bag or a pocket. There are various kinds of bags e.g. Handtaschen, Einkaufstaschen (plastic and paper ones synonymous with Tüten). https://www.duden.de/rechtschreibung/Tasche