The Mapbox directions API allows you to avoid motorways documentation.
Is there a way to do this in the Matrix API? It is not apparent that this is supported in the API documentation.
The Mapbox Matrix API does not provide a means for avoiding motorways. The Mapbox Directions API exposes an optional exclude parameter, documented in the table here, which can be set to motorway when the profile parameter is either mapbox/driving or mapbox/driving-traffic. There is no exclude parity for the Matrix API.