Is it an object clause? No. It doesn't (on its own) serve as an object. The entire phrase "clear evidence that smoking can lead to many diseases" serves as the complete object of the verb "has given". If we care about such things, the so-called simple object is the noun "evidence".
Is it a relative clause? No. Although the word "that" can be a relative pronoun, that isn't the way it behaves in this sentence. It doesn't serve any role within the clause "smoking can lead to many diseases". Instead, the word "that" simply marks the following clause as a content clause.
Is it an appositive clause? No. If it were an appositive, then "clear evidence" and "that smoking can lead to many diseases" would be two different ways of describing the same referent. In this case, the content clause refers to something which the evidence supports, not something which the evidence is.
Is it substantive or attributive? Since it describes an attribute of the evidence, I find the attributive label to be more sensible in this context. On its own, the clause could be substantive. In another sentence it might serve as a subject or an object. In this sentence, it restricts the meaning of the word "evidence".
Since the clause describes an attribute of a referent and restricts the meaning of a word, the label restrictive attributive clause seems both sensible and useful to describe the function of this content clause in context.