component.get(v.body) not working as expected

@Praveen, yes, this is totally normal. Here is what is happening:

When we say that the body attribute is defined on all components we mean that it's defined on the base <aura:component/> from which all components inherit. Here is a simplified version.

<aura:component/>
   <aura:attribute name="body" type="Aura.Component[]"/>
   {!v.body}
</aura:component>

As you can see, the base component outputs the body tag that it receives in its own body, otherwise, nothing would be rendered. Angular calls that process "transclusion", the inclusion of content from another context.

When you write this:

<aura:component>
    <div>Body part</div>
    <ui:button label="Push Me" press="{!c.printCmpBody}"/>
</aura:component>

You are setting the body tag of the parent component. Everything defined in your component is the "lexical definition", and it's passed to its parent. If you want to read it, you could use cmp.getSuper().get("v.body") but it's a deprecated API, and it will probably not work. However, that's the idea behind it.

Why is it working like this? Let's call your component c:myComponent and use it inside an app:

<c:myComponent>
   <i>Instance Part</i>
</c:myComponent>

This is equivalent to this format:

<c:myComponent>
    <aura:set attribute="body>
       <i>Hello</i>
    </aura:set>
<c:myComponent>

As you see, every component needs to receive an attribute body independently of what it defines internally. You can try this format, it does work, but it's unnecessary except to illustrate how to set the body of a component.

Now, your component can ignore its body attribute as in your original code, or it can use it like this:

<aura:component>
    <div>Body part</div>
    {!v.body}
    <ui:button label="Push Me" press="{!c.printCmpBody}"/>
</aura:component>

You can place the expression {!v.body} anywhere you want.

The rendered content will then be equal to the instance's v.body plus the component-defined lexical definition:

v.body = <i>Instance Part</i>
+
lexical scope = <div>Body part</div>{!v.body}...
=
Rendered: <div>Body part</div><i>Instance Part</i>...

You can get more information on how the attribute body works by looking at slides 24, 25, and 27:

Mastering the Lightning Framework - Part 1

And the explications are at around 15:00 minute here:

Mastering the Lightning Framework - Part 1

Example of usage

Parent Component

<aura:component description="TestComponent">
    <div>Body Parent</div>
    <div>Body Parent</div>
    <div>Body Parent</div>
    <div>Body Parent</div>

    <c:childComponnet>
        <aura:set attribute="body">
            <div>Body nested</div>
            <div>Body nested</div>
            <div>Body nested</div>

        </aura:set>

    </c:childComponnet>
</aura:component>

childComponent

<aura:component description="testComponent2">
<aura:attribute name="body" type="Aura.Component[]"/>
    {!v.body}
    <lightning:button variant="brand" label="show body" onclick="{!c.getComponentBody}"/>
</aura:component>

ChildComponnetController.js

({

    getComponentBody: function(cmp, event, helper) {
        var body = cmp.get("v.body");
        console.log(body);
    },

})

output is array of 3 objects