truth is, i think (as a portuguese speaker), that this sentence is an ambiguous one, as it surely would be in its portuguese equivalent: "as tesouras estão no gabinete". so, both "on my desk" and "in my desk" should be correct translations. it would all be differenciated through context analysis.
"Tijeras" (scissorS) is plural so you need a plural verb, "están" (they are). You use "estar" instead of "ser" because you are talking about location. You may want to take a look at these references: http://www.drlemon.com/Grammar/servsestar.html. http://www.diffen.com/difference/Estar_vs_Ser
Would "Mis tijeras están en el escritorio." also be understood to mean "my" desk?
I realize el is "the" instead of "my", but I know that there are many cases where Spanish uses the definite article (el/la/las/los) instead of the possessive adjective (mi/mis/tu/tus/su/sus).
For example, I know that when referring to body parts and clothing, Spanish uses the definite article:
- Me duele la cabeza (My head hurts)
- Arreglo el pelo (I comb my hair)
- Él rompió los anteojos (He broke his glasses)
- Llevo puesta la camiseta favorita (I'm wearing my favorite shirt)