Hi @Dhiran,
Could you please share more details about the Items proeprty of the Data Table control?
I have made a test on my side, and don't have the issue that you mentioned. The screenshot as below:

Set the OnSelect property of the "Available" button to following:
Set(filterValue, "Site Services - Available")
Set the OnSelect property of the "Lost/Stolen" button to following:
Set(filterValue, "Lost/Stolen")
Set the Items property of the Data Table control to following:
Filter('20181204_case5', 'Location/Status'.Value = filterValue) /* <-- 20181204_case5 represents my SP list data source*/
The GIF screeshot as below:
Please check if you have set proper value for the filterValue variable. Also please check if you have typed proper filter condition within your filter formula.
In addition, you could also consider take a try with the following workaround:
Set the OnSelect property of your first button to following:
ClearCollect(
FilteredResult,
Filter('YourDataSource', ColumnName="TextString1")
)
Set the OnSelect proeprty of your second button to following:
ClearCollect(
FilteredResult,
Filter('YourDataSource', ColumnName="TextString2")
)
Set the Items property of the Data Table control to following:
FilteredResult
Best regards,
Kris