clone-environment.ps1

$token = '<API_TOKEN>'
$sourceEnvironmentName = '<SOURCE_ENVIRONMENT_NAME>'

$headers = @{
  "Authorization" = "Bearer $token"
  "Content-type" = "application/json"
}

# get source environment ID
$sourceEnvironmentId = ((Invoke-RestMethod -Uri "https://ci.appveyor.com/api/environments" -Headers $headers -Method Get) | where {$_.name -eq $sourceEnvironmentName}).deploymentEnvironmentId

# get source environment properies
$source = Invoke-RestMethod -Uri "https://ci.appveyor.com/api/environments/$sourceEnvironmentId/settings" -Headers $headers -Method Get

# optionally update name
$source.environment.name = ($source.environment.name + "-new")

# create new environment with properies from the source
Invoke-RestMethod -Uri 'https://ci.appveyor.com/api/environments' -Headers $headers  -Body ($source.environment | ConvertTo-Json -Depth 10) -Method Post

Ilya, thank you for an example, please update for further usage:
FROM

$sourceEnvironmentId = ((Invoke-RestMethod -Uri "https://ci.appveyor.com/api/environments" -Headers $headers -Method Get) | where {$_.name -eq "iis2"}).deploymentEnvironmentId

TO

$sourceEnvironmentId = ((Invoke-RestMethod -Uri "https://ci.appveyor.com/api/environments" -Headers $headers -Method Get) | where {$_.name -eq $sourceEnvironmentName}).deploymentEnvironmentId

@PVXDevOps Thanks a lot, updated!