The two fulfil two different grammatical roles.
In unserer Klasse sind zehn Schüler, davon sind zwei Amerikaner.
As others have already pointed out, these are actually two sentences, two main clauses not connected by a conjunction and thus using a full stop between them is fine. We can thus take the second one by itself.
Davon sind zwei Amerikaner.
(Other word orders such as ‘Zwei davon …’, are fine too.)
Davon in that sentence is a demonstrative pronoun incorporating a preposition of the da- class. It is analogous to daher, dahin, dagegen, darauf and others:
Daher weht der Wind.
Dahin musst du laufen, um Rom zu erreichen.
Du musst deinen Kopf dagegen schlagen, dann geht vielleicht die Tür auf.
Du willst darauf klettern?
All of those can be translated by a corresponding preposition and a demonstrative pronoun such as that.
In unserer Klasse sind zehn Schüler, von denen zwei Amerikaner sind.
Here, von denen is an extended relative pronoun including a preposition. (Note that the preposition is the same as before.) The relative pronoun is slightly more emphasised than others would be. For example, replacing it with von ihnen, von welchen etc. puts less emphasis onto the Americans. Note that the second clause is now a relative one and can no longer stand on its own.
Using a preposition followed by a generic relative pronoun as in the example just now is not always considered the best style. Instead, there are special prepositional relative pronouns that are often considered better. In our case this would be:
In unserer Klasse sind zehn Schüler, wovon zwei Amerikaner sind.
This would be the wo- type of relative pronouns which can be considered a bridge between the demonstrative preposition-containing pronoun davon and the preposition plus relative pronoun von denen.