Why are Chinese not able to understand a foreigner if he makes a small mistake when speaking Mandarin, whereas I can understand foreigners making multiple mistakes in English and with funky accents?

Because even one tone error changes the meaning of the sentence completely.

In English, we put stress on different syllables.

economy - the stress is on the second syllable.
economist - the stress is also on the second syllable.
economics - the stress is on the third syllable.

I have come across non-native speakers of English who, when saying “economics”, place the stress on the second syllable. It sounds out of place sure, but I still know what they’re referring to.

Same with “photography”. The stress is on the second syllable. But I’ve encountered non-native speakers of English who place the stress on the first syllable. Still understandable. You know what they’re talking about.

But in Mandarin and Cantonese and other Chinese languages, you get one or two tones wrong, and not only do you change the word, but the entire meaning of the sentence changes as well.

For example:

今天是星期日 (Jīn tiān shì xīng qī rì.) - Today is Sunday.
今天是行乞日 (Jīn tiān shì xíng qǐ rì.) - Today is begging day.

Another more common example would be:

熊猫 (xióng māo) - Panda
胸毛 (xiōng máo) - Chest Hair

A short comic on what might happen if you get the tones mixed up:
(Source: yoyochinese.com)

It’s similar in Cantonese, and every Chinese language.

In Cantonese, you can order this green leafy vegetable at a restaurant:

菜心 (coi3 sam1)

But if you get the tones wrong, and say:

除衫 (ceoi4 saam1)

you’ve just told the waiter or waitress to take off their clothes.
Not exactly a common action for a waiter or waitress to carry out at restaurants.
Well, at least at the restaurants I frequent :D

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Conclusion: Because of its tonal nature, one tone error in Mandarin or any of the Chinese languages can change the meaning of the sentence completely. If you didn’t have a whole lot of context to work with prior, it can be very confusing.

On the tonal language spectrum, Mandarin is on one end of the spectrum and is a truly tonal language.

English is several steps away from that, and is generally considered to be a stress-accent language

Therein lies your predicament.