Quarter calculation upto selected month

First make sure that your date table has a date column which uniquely identifies the year and month. In my example I am using 'Date'[Start of month], but you could equally use end of the month. The key point is that it is of type date, so that MAX will work correctly.

Create a disconnected copy of the date table. It should not have a relationship to any other tables, it is only for use in the slicer. In my example I call the table 'For Slicer'.

Use 'Date'[Year] and 'For Slicer'[Month name] in separate slicers. In your chart visual, use 'Date'[Quarter].

Create a measure like

My Measure = 
VAR MonthInSlicer = CALCULATE(
    MAX( 'For Slicer'[Start Of Month] ),
    TREATAS( VALUES( 'Date'[Calendar Year Number] ), 'For Slicer'[Calendar Year Number] )
)
VAR DateToUse = CALCULATE(
    MAX( 'Date'[Start Of Month] ),
    KEEPFILTERS( 'Date'[Start Of Month] <= MonthInSlicer )
)
VAR Result = CALCULATE(
    [Base Measure],
    'Date'[Start Of Month] = DateToUse
)
RETURN Result

where [Base Measure] is whatever you are trying to compute. You could also turn this code into a calculation item, and call SELECTEDMEASURE() instead of [Base Measure].

You need to use a disconnected table or the other quarters will not be v isible. Filters coming from a related table or from the same table will show only the rows that's been selected so if you select August, you will see Q3 only,.