When you take out money from your Cash account, you have to record it by opening Banking > Write Cheques, which is similar to literally write cheques/withdraw money, except that you take it out from your Cash/Petty Cash account.  Make sure you select Cash/Petty Cash account.
The screenshot below is an example of cash disbursement of $113,- of Supplies:Marketing taken out of Petty Cash account, paid to Davies Supply.

 

QB Tracking Cash

 

For those of you who are familiar with account register window, you can use your checking account register in Banking > Use Register  to move amount from your checking to your Cash/Petty Cash account.  
Similarly, you can use your Cash/Petty Cash account register to record your cash expenditures.