Is it possible to cancel a Azure DevOps pipeline Job programmatically?

You can cancel a build through REST API:

PATCH https://dev.azure.com/atbagga/atbagga/_apis/build/Builds/120
Request content: {'status': 'Cancelling'}

Here you have an example:

steps:
- task: PowerShell@2
  name: ConditionalStep
  inputs:
    targetType: 'inline'
    script: |
      Write-Host "I'm here"
      Write-Host ('$(SomeVariable)' -eq 'Stop')
      if ('$(SomeVariable)' -eq 'Stop') {
        $uri = "https://dev.azure.com/thecodemanual/DevOps Manual/_apis/build/builds/$(Build.BuildId)?api-version=5.1"

        $json = @{status="Cancelling"} | ConvertTo-Json -Compress

        $build = Invoke-RestMethod -Uri $uri -Method Patch -Headers @{Authorization = "Bearer $(System.AccessToken)"} -ContentType "application/json" -Body $json

        Write-Host $build
      }
      Write-Host "And now here!"
    pwsh: true
- pwsh: Start-Sleep -Seconds 60    
- task: PowerShell@2
  inputs:
    targetType: 'inline'
    script: |
      $uri = "https://dev.azure.com/thecodemanual/DevOps Manual/_apis/build/builds/$(Build.BuildId)/timeline?api-version=5.1"

      Write-Host $uri

      # Invoke the REST call
      $build = Invoke-RestMethod -Uri $uri -Method Get -Headers @{Authorization = "Bearer $(System.AccessToken)"} -ContentType "application/json"

      $taskResult = $build.records | Where-Object {$_.name -eq "ConditionalStep" } | Select-Object result

      Write-Host $taskResult.result

    pwsh: true

For that you will get that output:

If you get such error:

 | {"$id":"1","innerException":null,"message":"Access denied.
 | DevOps Manual Build Service (thecodemanual) needs Stop builds
 | permissions for vstfs:///Build/Build/1611 in team project
 | DevOps Manual to perform the
 | action.","typeName":"Microsoft.TeamFoundation.Build.WebApi.AccessDeniedException, Microsoft.TeamFoundation.Build2.WebApi","typeKey":"AccessDeniedException","errorCode":0,"eventId":3000}

Please make sure that your build account has permission to stop a build:

You will find this under this section:

Please note

What you can't do is set a build as completed. If you dod this. Whole pipeline will be still executed. So if this isn't what you want, you need to add condition to every step with an output variable set previously in the pipeline and in that way ignore those steps.

steps:
- task: PowerShell@2
  name: ConditionalStep
  inputs:
    targetType: 'inline'
    script: |
      Write-Host "I'm here"
      Write-Host ('$(SomeVariable)' -eq 'Stop')
      if ('$(SomeVariable)' -eq 'Stop') {
        Write-Host '##vso[task.setvariable variable=shouldStop;isOutput=true]Yes'
      }
      Write-Host "And now here!"
    pwsh: true
- pwsh: Start-Sleep -Seconds 60
  condition: ne(variables['ConditionalStep.shouldStop'], 'Yes')
- task: PowerShell@2
  condition: ne(variables['ConditionalStep.shouldStop'], 'Yes')
  inputs:
    targetType: 'inline'
    script: |
      $uri = "https://dev.azure.com/thecodemanual/DevOps Manual/_apis/build/builds/$(Build.BuildId)/timeline?api-version=5.1"

      Write-Host $uri

      # Invoke the REST call
      $build = Invoke-RestMethod -Uri $uri -Method Get -Headers @{Authorization = "Bearer $(System.AccessToken)"} -ContentType "application/json"

      $taskResult = $build.records | Where-Object {$_.name -eq "ConditionalStep" } | Select-Object result

      Write-Host $taskResult.result

    pwsh: true