Is it possible to make an md-button smaller?

Try the following class in your styles. You can adjust the pixel depending on how big/small you want the button to be.

.md-button.md-small {
     width: 20px;
     height: 20px;
     line-height: 20px;
     min-height: 20px;
     vertical-align: top;
     font-size: 10px;
     padding: 0 0;
     margin: 0;
}

Add the following to your styles:

.md-button {
    min-width: 1%;
}

Alternatively, use a custom class:

.md-button.md-small {
    min-width: 1%;
}

Or, in Angular Material 2:

.mat-button.mat-small {
    min-width: 1%;
}