Delete Customer Address by address id Programmatically Magento 2.

You can delete the specific customer address by address id using the AddressRepositoryInterface interface.

Magento\Customer\Api\AddressRepositoryInterface contains the deleteById($addressId) function with pass first argument as address id to fetch specific customer address data.

<?php
namespace Rbj\Model\Address;

use Exception;
use Magento\Customer\Api\AddressRepositoryInterface;

class Delete
{
    /**
     * @var AddressRepositoryInterface
     */
    private $addressRepository;

    public function __construct(
        AddressRepositoryInterface $addressRepository
    ) {
        $this->addressRepository = $addressRepository;
    }

    /**
     * @param int $addressId
     *
     * @return bool
     */
    public function deleteCustomerAddressById(int $addressId)
    {
        $error = false;
        try {
            $this->addressRepository->deleteById($addressId);
        } catch (Exception $e) {
            $error = true;
            throw new Exception($exception->getMessage());
        }
        return $error;
    }
}

You can delete the specific customer address by the above function by passing the address id as the first argument.

$addressId = 10;
$address = $this->deleteCustomerAddressById($addressId);