Having seen your markup above, I assume that you have already tried interpolation, and it does not work. Just a thought - would it be extend in this context ? those. expand individual mixers button-*with a certain roundness.
$color , , mixin ! , button-blue... button-tree mixins, , $circle?
, , button-blue... button-tree button, , " ifs", ,
@function include-button-mixin($color) {
@if $color == blue
@include button-blue
...
}