Answering the original question where at most two "-" separators occur:
=LEFT(A1,FIND("-",A1,FIND("-",A1)+1)-1)
Answering the modified question where an arbitrary number of "-" separators occur:
=LEFT(A1,FIND("|",SUBSTITUTE(A1,"-","|",LEN(A1)-LEN(SUBSTITUTE(A1,"-",""))))-1)
This answer is via How can I perform a reverse string search in Excel without using VBA?, where several adaptable options may be found as well.
This is very clever, but with a little VBA a more straightforward answer could be devised. The VBA to do this can be very simple, but I recommend bringing in Regular Expressions for more flexible solution you can use on other similar problems.
Function RegExReplace(pattern As String, sourceString As String, replaceVar As String) As String
Dim RE As Object
Set RE = CreateObject("vbscript.regexp")
RE.pattern = pattern
RE.Global = True
RegExReplace = RE.Replace(sourceString, replaceVar)
End Function
Then in your worksheet you would use
=RegExReplace("-[^-]*$",A1,"")