First of all you need to buy the inventing bench in the hobby section of buy mode. This is the first step in order to find a pink gem. When you invent the first thing, you would be able to make a new object. Your player will build something new instead of the same thing. After inventing few objects, you will unlock an object known as miner.
After unlocking this object, do not sell it but place in your inventory. Go outside and place the object on the ground. Then tell your character to dig with the miner. After digging you will find many rare gems including the pink diamond.
Finding the pink diamond
When you start digging, you will find different gems. It may take some days but continue digging until you seek the pink diamond. This method is faster than visiting other town for gems.
In case you do not want to collect diamonds, sell them for money but keep the pink diamond with you. Remember you will most commonly find normal diamonds while digging instead of pink.
Unlocking the heart shaped cut
After finding the pink diamond, you need to unlock the heart shaped cut as the original diamond will be ore shaped. You need to complete the ‘Gem Collector’ challenge in order to unlock the heart-shaped cut. For this you need to find all the ten different gems.
Send the gem to a jeweller
Next you need to select a pink diamond you collected earlier. Select ‘Have Gem Cut’ and then click ‘Heart-Shaped Cut.’ By doing this, your character will send the pink diamond to a jeweller. After few in-game days you will receive a heart-shaped pink diamond in your mailbox.
When received, you can sell the heart-shaped pink diamond for almost $8000 or display in your Sims home lot.