Why does the mind always want to 'do something' and how to cultivate 'non-doing'? There is a Zen saying, 'Sitting quietly, doing nothing, Spring comes, and the grass grows, by itself' by Basho.

But I have observed the nature of my mind that it always wants to 'do something', it finds respite only when I apply it to solve problems. Why does doing nothing just sitting makes me feel like I am wasting my time? OR am I taking the teaching of Basho in the wrong way?

How can I train my mind to just be?  

Edit: I am asking about all the time when I am not meditating.
Why does doing nothing just sitting makes me feel like I am wasting my time? 


There may be several reasons for this, and i can't say what is relevant in your particular case. However, generally speaking, the feelings you are describing is the consequence of one or several conditioned causes listed below:


the assumption that it is wrong to spend time reflecting on your inner workings
the assumption that self worth is only built on being productive
the fact that you are facing real problems that require real solutions
something else, yet to be discovered



  OR am I taking the teaching of Basho in the wrong way?


It seems that you have caught on to something in Bashos quote. Have you asked yourself why that interests you?


  How can I train my mind to just be? 


It seems to me that your training already has begun, because you are reflecting on these tendencies and asking the right questions (from a buddhist understanding) as far as i can tell. 

Roughly speaking, training to "just be" from a buddhist framework builds on:


meditation and investigating these thoughts, emotions and tendencies (samadhi), 
studying what is truly helpful according to buddhism (panna), and also 
making the habitual adjustment for improved wellbeing for yourself and others (sila)


A good continuation would be a meditation called anapanasati (perhaps you're already familiar with it). More information about how and why it is recommended can be found here: 

https://www.accesstoinsight.org/lib/authors/ariyadhamma/bl115.html