I spent $180 during my month in Iceland. I spent ~$400 during my month and a half in mainland Europe. It is absolutely possible to travel on a mini budget. You just may not be comfortable the whole time. Fortunately, lack of comfort is a catalyst for adventure.
How I saved money:
Food - I brought freeze-dried food from the US to eat in Iceland, I carried this with me until I finished it. I bought one canister of stove fuel and found another full one in a fuel canister recycling bin. When I bought more food, I went to cheap grocery stores (Bonus in Iceland, Tesco in England, various stores in France and Italy) and bought cheap ingredients and calorie foods. I ate from restaurants around 10-15 times during the trip. Sometimes those I traveled with offered me food or took me to restaurants, for which I was extremely grateful. I also dumpster dived a few times in Iceland, getting things like bread, cake, and orange juice that was all still quite fresh. I did not eat well overall, I should have treated my body better by feeding it more. An extra $50 investment in food overall would have solved that problem.
Lodging - I payed for three nights of lodging: one campsite in Iceland, two nights in a cheap London hostel. Other than these three nights, I camped in my tent or stayed with people I either met on the road or had contacted for a place to stay. This happened more than one would expect. I spent fifteen nights indoors because of the generosity of others.
Baggage - I was able to operate in this way primarily because I traveled with one 65 liter backpack. I could easily bring everything I had into other people's cars or move into mountainous, unpopulated areas on foot. I also carried a compact REI daypack I used when doing day-trips with a homebase.
Transport - I payed for transit from the Keflavik airport (that was a mistake, I should have hitched directly from the airport), inner city buses and subway transit in Rekjavik, London, Nottingham, Paris, Perugia, and Rome, and for two train rides. The majority of the distance was covered through hitchhiking, the cheapest (and most rewarding) option available for land travel. There was certainly also time spent walking and I boarded a few trains in France and Italy, but ~85% of land was covered while hitching. Many of the best parts of the trip came from hitchhiking, meeting people, and having experiences I never would have expected to have through those interactions.
Plane tickets - Bought early. Flying to England seemed to be the cheapest way to get to mainland Europe from Iceland, so I flew there. I used Wow air for the Iceland-England trip. The return ticket from Rome was expensive, roughly the same price as the US-Iceland ticket and the Iceland-England ticket combined, not so good. If you want to get to Europe and back as cheaply as possible, do a round-trip to London or Paris with Wow Air, buying far in advance. Just make sure you are able to get back to the city in which you arrived by the end of your trip.
Mementos - I brought back pictures and videos, an ice axe I found on a glacier and several volcanic rocks. I had no interest in souvenirs, I assume no one else at home did either, so I stayed away from them. I also had a small notebook I used to record the journey.
Museums - Went to free ones as much as possible, but the larger museums in Italy did get a bit expensive. I did pay full price and then some for a ticket to the Vatican Museum, though one might say it was worth it as I was with a group and pressed for time. I visited five different art galleries in downtown Reykjavik, the Tate Modern and the National Watercolor Gallery in London, The Louvre and the Petit Palais in Paris, the Uffizi and the Accademia Gallery in Florence, the Vatican Museum and the Capuchin Crypt along with several free churches with Caravaggios in Rome.
I intend to be just as cheap when I return to Iceland this upcoming summer in August. It's a wonderful way to live, and the easiest way to force myself to meet others, think quickly, and be flexible. The fact that you save money is just a bonus.