To me this sounds like "vidite me hopsa?"
Well, but “hopsa” doesn’t make any sense.
So the noun "dog" is treated the same as a masculine person in Czech noun cases?
In every day use what is more common or better to say? Vidite meho psa or vidite moje pes?
The form "moje" would be correct with a neuter noun in the accusative singular, but "pes" is masculine, so must use "mého" in the accusative singular.
It's definitely the first option. The second one is not grammatically correct. The latter would work in plural (if you changed it a bit). If you had more dogs, you could ask: "Vidíte moje psy?"