Is there any way to disable or stop a particular resource group temporarily? I know we can delete the resource group or we can stop certain services under the resource group but I am unable to find a way where I can just shut down the resource group or all of it's resources at once, temporarily.
This does not seem to be possible at the moment but a request has been made here, however, no response from Microsoft on what it's status.
In general, if there are features that are not available in e.g. Azure, use the feedback site to suggest and vote on new features.
However, if you only got some specific type of resources in your resource group, like e.g. virtual machines, then you can stop them all in one PowerShell command like this:
Get-AzureRmResourceGroup <group name> | Stop-AzureRmVM -Force
Note: this approach is dependent on the type of resource and not a generic solutions