Stop iOS opening last session in browser
You misunderstand what swiping up on an app does. Swiping up on an app from the app switcher causes its temporary data to be unloaded from your device's RAM (RAM, short for random-access memory, is your device's short-term memory). However, data from tabs in any browser is stored as permanent data (just like game data and text messages are permanently stored, tabs are too), and this permanent data is unaffected by a RAM unload. Unloading an app from the RAM (swiping up on it) is designed to fix issues caused by app data in the device's short-term memory, not to unload data from an app's place in your device's long-term memory, which is where browser data is stored. 

Unlike the common myth goes, apps like Facebook and Google Maps can still run in the background even after being closed (swiped-up upon); it is up to them to stop using background data. Force-closing an app by swiping up on it unloads short-term data (like how UI elements moved or changed after app-launch) but does not affect any stored data or background app usage. Swiping up doesn't shut an app down.

In iOS 10, Apple's upcoming version of iOS set to be released in the fall, there will be a button accessed by long-pressing on the tab-button to close all tabs. Why this doesn't exist in iOS 7-9 is a mystery.

So for now, you'll just have to close your tabs one-by-one or just leave them all open*.

*or switch to Android, where the default browser (Chrome) lets you close all tabs at once. And sadly, Chrome for iPad does not have this feature.

Edit: My advice is to try other iPad browsers (I personally like Brave Browser and Dolphin Browser) and check if they have a similar option to close all tabs at once; try long-pressing on the X of one tab, or going into the tab switcher.