Most answers are - sorry - plain wrong. With this exception:
The purpose of a DI is to change instrument level to mic-level, the reason is that mic-level signals don't degrade in quality even over very long cable-lenghts (up to a mile and more). So if you want to connect the DI out of an amp or a dedicated DI-box to a mixer, you have to use the mic-input and in this case the XLR-in. It is nonsense to connect the output of a DI to the line-in - in this case TRS - of a mixer.
Mic-ins don't have to be XLR and line-ins don't have to be TRS, but in most cases they are.
I don't see the problem. XLR from the amp DI output into XLR on the mixer. Then use the mic channel input gain to set the correct gain into the channel. You may need to turn the gain down quite a bit, but that's why the control is there.
The purpose of a DI is to change instrument level to mic-level, the reason is that mic-level signals don't degrade in quality even over very long cable-lenghts (up to a mile and more). So if you want to connect the DI out of an amp or a dedicated DI-box to a mixer, you have to use the mic-input and in this case the XLR-in. It is nonsense to connect the output of a DI to the line-in - in this case TRS - of a mixer.
Mic-ins don't have to be XLR and line-ins don't have to be TRS, but in most cases they are.