What did Griffith mean when he said "you are mine" to Guts? Mind to help me with this curiosity? Griffith acts differently after Guts decides to leave. He says, "you are mine" to him. 

Was this to imply that he was gay for Guts? Ever since they have first met, it confuses me.
You have to remember how Guts first joined the Band of the Hawk. Guts challenged Griffin to a duel, and Guts agreed to join the band as his subordinate if he lost.  



Before this Griffin even told Guts: "I want you", which Guts misinterprets as a gay thing, and Griffin explains how he views him as a military asset with an interesting willingness to risk his life.  

This is the sense in which Guts is "his".  His membership is guaranteed by the conditions of the duel, and Guts has not won a release from this obligation. This is why Guts and Griffith then fight again when Guts decides to leave.

A lot could be said and debated about whether or not Griffith has sexual or romantic feelings for Guts.  It's not implausible, but you have to keep in mind that Griffin is consistently portrayed as a narcissistic sociopath.  Sex, sexuality, and personal attachments in general are just tools to him. Part of his frustration and eventual breakdown over Guts's leaving is because Griffin views it as proof that he's allowed himself to grow weaker and soft.  He does realize that somehow Guts became more important than his lifelong dream; a dream he had been willing to sacrifice anything for, and had thought this included Guts and the rest of the Band. But he doesn't seem to experience this as "love for Guts" but rather "disgust with himself", as befits his narcissism.