"I copied the model. And then when I modify it, it also changes to the original one."

In this case, you want to [Clone] the model, not [Copy].
When you [Copy] the models, copied models and original models are still identical. Hence when you modify one model, the change will apply to the other. On the other hand, [Clone] will make a completely different model based on the original model. So even though you modify one, the change will never apply to the other.

- How to clone models
You can clone models in the structure tree. Let's clone the "Monitor" class with one attribute and two operations in the figure below.

















Right-click on the "Monitor" Class to open its Pop-up menu and then click [Clone].




























Cloning the "Monitor" succeeded. The cloned model is "Monitor_0". Its attributes are also cloned, they are the same name as original ones but completely different models. So modifying one does not affect to the other.


















Cloneable models in Astah Professional and UML
Package, Subsystem, Model, Class, Attribute, Operation, UseCase, Actor, Interface, Entity, Boundary, Control, Component and Node
Clonebale models in Astah Professional only
ER Entity (Primary key, Attribute), Domain, Datastore, External Entity, Requirement and TestCase

Astah Community currently does not have an ability to clone models unfortunately.
To try out Astah Professional or UML, download our free trial from here.

Cheers,
Satomi