Translation:I think this is mine.
A nice guess, but it's really just a grammatical rule. When と acts as a particle indicating something that is thought/said/expressed, the verb preceding と is in plain form, and the final verb determines the politeness of the sentence as a whole. For example: かれはとしょかんに行くといいました -> "He said he's going to the library".
There are essentially two sentences in one sentence here これは。。。とおもいます - 'I think ....this thing' and わたしのだ 'it is mine'. わたしのだ is a subordinate clause within the main clause or sentence and it is also reported speech - or in this case 'reported thought". The と before the verb indicates the speaker's thought/s or in other words it lets us know that the subordinate clause that precedes it is reported speech/thought. Verbs in reported speech are in plain form hence we have だ instead of です. Hope this makes sense?