Try clearing the config cache and run the below commands to delete your Search Service Application.
#Get ID for the Search Service Application
Get-SPServiceApplication
# Paste the service application ID in place of searchserivceapplicationid
Remove-SPServiceApplication searchserivceapplicationid -removedata
If the above commands didn't work for you try with the below commands again.
Get-SPServiceApplication
STSADM.EXE -o deleteconfigurationobject -id <GUID of the service>
Below article for more information to delete corrupted search service application.
https://blog.greenbrain.de/2013/11/removing-corrupted-search-service-from.html
Thanks & Regards,