Some friends here on the Hyper-V team shared a PowerShell 2.0 script for deleting a VM snapshot:

However BEFORE you go deleting snapshots, please read the Hyper-V Snapshot FAQ, and have a look at the Ben Armstrong Snapshot FAQ Video. 

# Delete Virtual System Snapshot

param(
    [string]$vmName = $(throw "Must specify virtual machine name"),
    [string]$vmSnapName = $(throw "Must specify snapshot name")
)

# Get the virtual machine by name
$vm = gwmi -namespace root\virtualization Msvm_ComputerSystem -filter "ElementName='$vmName'"

# Get the setting data for the snapshot by name
$snapshot = get-wmiobject -namespace root\virtualization Msvm_VirtualSystemSettingData `
    -filter "SystemName='$($vm.Name)' and SettingType = 5 and ElementName = '$vmSnapName'”
if($snapshot -eq $null -or $snapshot -is [array]){
    throw "Unable to find single snapshot with name `"$vmSnapName`""
}
# Get the management service and apply the snapshot
$vmms = gwmi -namespace root\virtualization Msvm_VirtualSystemManagementService

$result = $vmms.RemoveVirtualSystemSnapshot($snapshot)

if($result.ReturnValue -eq 4096){
    # A Job was started, and can be tracked using its Msvm_Job instance
    $job = [wmi]$result.Job
    # Wait for job to finish
    while($job.jobstate -lt 7){$job.get()}
    # Return the Job's error code
    return $job.ErrorCode
}
# Otherwise, the method completed
return $result.ReturnValue

 

For more info on how to use PS cmdlets see: http://www.microsoft.com/technet/scriptcenter/topics/msh/cmdlets/index.mspx

See also James O’Neil’s New and improved PowerShell Library for Hyper-V. Now with more functions and... documentation!

For all 35 sample Hyper-V PS1 scripts in a zipfile, go to: Hyper-V%20PowerShell%20Example%20Scripts.zip-download