How can I devise a means of determining service level percentage that omits the most recent month using Power BI?

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One way to accomplish this is to create a calculated measure that excludes the most recent month's data from the calculation of the service level percentage.

Assuming you have a date field in your data model, you can use the following DAX formula to create the calculated measure:

Service Level Percentage (Excluding Most Recent Month) =
VAR MaxDate = MAX('Table'[Date])
VAR ExcludedData = CALCULATE(SUM('Table'[Completed]), 'Table'[Date] = MAXDate)
RETURN
DIVIDE(
  CALCULATE(SUM('Table'[Completed]), 'Table'[Date] < MaxDate) - ExcludedData,
  CALCULATE(SUM('Table'[Target]), 'Table'[Date] < MaxDate)
)

In this formula, Table is the name of your table, Date is the name of your date column, Completed is the name of the column containing the completed service requests, and Target is the name of the column containing the target number of service requests.

The formula first calculates the maximum date in your data model and saves it in a variable called MaxDate. It then calculates the sum of completed service requests for that maximum date and saves it in a variable called ExcludedData.

The actual service level percentage is then calculated by subtracting the ExcludedData from the sum of completed service requests for all dates before the MaxDate, and dividing by the sum of target service requests for all dates before the MaxDate.

You can then use this calculated measure in your Power BI visualizations to show the service level percentage excluding the most recent month.