No. Unlike English "and/or", case particle と is not a conjunction, which can connect clauses as well as nouns. It works only when it's combined with a noun.
In Japanese grammar, you need the verb in the modifying clause to be an attributive form, in short, する, した, やさしい and きれいだ are to be する, した, やさしい and きれいな respectively.
So, you can express your example as 牛乳を買った、ガソリンを買わなかった男は寝た. This is one form of solution. (Commas are optional.)
However in practice, you will more often see the former verb is changed into 買い (conjunctive form) or 買って (te form), which technically function as an adverb that modifies the latter 買わなかった and eventually can modify the 男 through 買わなかった. i.e. 牛乳を買い、ガソリンを買わなかった男, which is the second solution.
The third solution is to use conjunctive particles like …が or …けれども. These particles need to be used with a terminal form of verbs (する、した、やさしい、きれいだ). i.e. 牛乳は買ったがガソリンを買わなかった男
(note: you can't use conjunctive particle …し in a modifying clause, in short, you can say あの人はきれいだし、やさしい for "S/he is beautiful and kind" while you can't say きれいだし やさしい人 for "a beautiful and kind person".)