Negation in the indicative mood is formed by adding δεν (not); no auxiliary verb needed. Αυτή υποστηρίζει = She supports. Αυτή δεν υποστηρίζει = She does not support. Then you add the object in the right place.
Note that negation in the subjunctive uses μην as 'not'. The imperative also uses subjunctive forms in negation.