Create the New-AzureStorageContext  and use the below command to delete the files.

----Creating Azure Storage Context---
Import-Module "C:Program Files (x86)Microsoft SDKsAzurePowerShellServiceManagementAzureAzure.psd1"
Import-AzurePublishSettingsFile C:AzureAzure_credentials_file.publishsettings
$subscriptionName = "Subscription Name"
$storageAccountName = "Storage Account Name"
Select-AzureSubscription $subscriptionName
$storageaccountkey = get-azurestoragekey $storageAccountName | %{$_.Primary}
$destContext = New-AzureStorageContext -StorageAccountName $storageAccountName -StorageAccountKey $storageaccou...

Get-AzureStorageBlob -Container containerstorage -Context $destContext

Get-AzureStorageBlob -Container containername -Context $destContext