No, it wouldn't most of the time. Это не твоё means that something is not yours, and the speaker is not specifying the gender of the object, so it can be applied to any object and even several objects as a whole.
On the other hand, you can use gender specific sentences, but those will be different.
For instance, let's say, you tell me: No, the spoon is not yours. A spoon is feminine in Russian, so you can say: Нет, ЭТА ложка не ТВОЯ. or in short: It is not yours= ОНА не ТВОЯ.
Now, if I want to say No, the chair is not yours. The word chair is masculine, so it will be Нет, ЭТОТ стул не ТВОЙ. Or in short: It is not yours= ОН не ТВОЙ.
The neuter example. No, this bucket is not yours. Нет, ЭТО ведро не ТВОЁ. Short version: It is not yours = ОНО не ТВОЁ.
Finally, a plural example. No, they are not your books. Нет, ЭТИ книги не ТВОИ. They are not yours. ОНИ не ТВОИ.
To conclude, you can either say Это не твоё for any thing and you don't need to worry about its gender and number (which may be way easier for you at first), you can use gender specific sentences, but then you need to be careful.
P.S. there are some contexts where you indeed may say Эта не твоя, but it is a very specific case, where you have several things and you're saying that all of them belong to someone, but not that particular one. So, I'll probably include all of those as accepted translations but I warn you to be careful using them.