In Power Query, use some of the date functions.
To get the year it will be
Date.Year([monthyear])
For the month, it will depend on how you want to format it. Using the month of June as an example:
To get 'Jun'
Date.ToText([monthyear],"MMM")
To get the month number in the format 06
Number.ToText(Date.Month([monthyear]), "00")
Just to get the number 6 it will be:
Date.Month([monthyear])
In DAX use the date functions
For year the calculated column will be:
YEAR([monthyear])
For the month:
MONTH([monthyear])
I would always do a much data transformation in Power Query when you can before it gets to the data model.