In Chabacano, people do not say !Dios mio¡ when they say "my God" as one would in Spanish. When we say "my God", we say Señor!
Here are some situations wherein you would use the Chabacano Señor and sample sentences along with their rough English translation:
Señor, yo ya daw hace conese!
My God, let me do it! (let me be the one to do it)
Señor! *Cosa ese? (*pronounced as cosase)
My God, what is that?
Señor, tiene ladron na otro lao casa.
My God, the house on the other side is being robbed.
*literally there's a burglar at the house on the other side
*In Chabacano, one says el otro lao casa to mean your neighboring house
Señor, bueno ya lang ya llega ya tu.
My God, it's a good thing that you have already arrived.
The word Señor can also be a stand alone word. The way you say Señor would tell the emotion you are conveying.
I remember reading on the internet that in Spanish (I'm not sure if it's Mexican Spanish), when talking to God (in prayers), one would use the word Señor. In Chabacano, Señor is used in prayers instead of the word Dios. Any hispanohablantes out there who can shed more light on this is very much welcome to comment.