"You look the same as your mother."
Translation:Vypadáš stejně jako tvá matka.
svůj belongs to the subject of the sentence. What is confusing here is that "jako tvá matka." is actualy shorthand for "jako vypadá tvá matka.". So that stub that is not really a full clause still behaves like a clause for our purpose. And the subject there is implicit "ona" or "matka". So "svá/svoje matka" would be "her own mother". And that does not make sense here.