How to split the months to filter.

Anonymous , so if looking for a slicer that you select July in one and another slicer will have jun. That is not possible.

If you looking for two independent slicers for comparison refer to this. ( use month in place of date range)

https://community.powerbi.com/t5/Community-Blog/Comparing-Data-Across-Date-Ranges/ba-p/823601

In case you want MTD and LMTD, then use time intelligence. tat you can do with one slicer

MTD Sales = CALCULATE(SUM(Sales[Sales Amount]),DATESMTD('Date'[Date]))
last MTD Sales = CALCULATE(SUM(Sales[Sales Amount]),DATESMTD(dateadd('Date'[Date],-1,MONTH)))

Power BI — MTD Questions — Time Intelligence 3–5
https://medium.com/@amitchandak.1978/power-bi-mtd-questions-time-intelligence-3-5-64b0b4a4090e

To get the best of the time intelligence function. Make sure you have a date calendar and it has been marked as the date in model view. Also, join it with the date column of your fact/s. Refer :
https://radacad.com/creating-calendar-table-in-power-bi-using-dax-functions
https://www.archerpoint.com/blog/Posts/creating-date-table-power-bi
https://www.sqlbi.com/articles/creating-a-simple-date-table-in-dax/

See if my webinar on Time Intelligence can help: https://community.powerbi.com/t5/Webinars-and-Video-Gallery/PowerBI-Time-Intelligence-Calendar-WTD-YTD-LYTD-Week-Over-Week/m-p/1051626#M184


Appreciate your Kudos.

You could try the following method if you just want to create two buttons that act as a slicer. 

https://www.youtube.com/watch?v=0m-PCX1uCG4