Disclaimer: I come from a Windows background, my expertise in linux is quite slim.
In my home lab I had a requirement to update a software package which dropped support for php 7.0, which meant I needed to upgrade to 7.1 prior to upgrading the application.
Here are the steps that worked for me:
First stop the web server, in my case apache.
sudo service apache2 stop
Get a list of the current php packages you are using
dpkg -l | grep php
Add the repo, install the base packages, followed by the extra ones you were using with 7.0 ( my packages may differ from yours)
sudo add-apt-repository ppa:ondrej/php sudo apt-get install php7.1 php7.1-common sudo apt-get install php7.1 php7.1-cli php7.1-common libapache2-mod-php7.1 php7.1-mysql php7.1-curl php7.1-mcrypt php7.1-json php7.1-mbstring php7.1-bcmath php7.1-zip php7.1-intl php7.1-opcache php7.1-readline
Reconfigure apache2 for php 7.1 and restart the service
sudo a2enmod php7.1 sudo service apache2 restart
check that php 7.1 is now running
php -v PHP 7.1.8-2+ubuntu16.04.1+deb.sury.org+4 (cli) (built: Aug 4 2017 13:04:12) ( NTS ) Copyright (c) 1997-2017 The PHP Group Zend Engine v3.1.0, Copyright (c) 1998-2017 Zend Technologies with Zend OPcache v7.1.8-2+ubuntu16.04.1+deb.sury.org+4, Copyright (c) 1999-2017, by Zend Technologies
remove your old 7.0 packages
sudo apt purge php7.0-cl php7.0-bcmath php7.0-common php7.0-curl php7.0-intl php7.0-json php7.0-mbstring php7.0-mcrypt php7.0-mysql php7.0-opcache php7.0-readline php7.0-zip