After a bit of playing around and testing (never used slicers through VBA before) I worked out the below.
However, be advised that a slicercache can have slicers on different worksheets. A slicer is linked to a slicer cache which in turn is linked to a data source (e.g. a pivot table). If any slicer is changed, then the slicer cache is changed which changes the pivot table as well. You cannot have 1 slicer with a filter on and another slicer linked to the same pivot table with a filter off, as the pivot table is updated by a slicer's filters. It would't make sense. ;-)
What does make sense is having multiple slicers and multiple pivot tables - using the below will indeed clear the filters for one slicer / cache / pivot but not change any others. This is the only way it could work so hopefully that was what you wanted anyway!!
Sub test()
RefreshSlicersOnWorksheet ActiveSheet
End Sub
Public Sub RefreshSlicersOnWorksheet(ws As Worksheet)
Dim sc As SlicerCache
Dim scs As SlicerCaches
Dim slice As Slicer
Set scs = ws.Parent.SlicerCaches
If Not scs Is Nothing Then
For Each sc In scs
For Each slice In sc.Slicers
If slice.Shape.Parent Is ws Then
sc.ClearManualFilter
Exit For 'unnecessary to check the other slicers of the slicer cache
End If
Next slice
Next sc
End If
End Sub