DAC Signal Clipped By DC Voltage Source
OP oscillograph shows clipping of the bottom peak of the sinusoidal wave. This suggests that the internal buffer can only source current, and cannot sink current. A load resistor is required to pull the buffer output down. An internal pull-down resistor is included.

From the data sheet spec, the 5k minimum pull-down resistor combined with \$V_{REFHI}\$ of +3.3V, the buffer could source at least 0.66 mA. No data sheet spec of how much current it can sink. 

Data sheet does specify a settling time of 2 microseconds when slewing from 0.3V -to- +3V with 100pf load. This spec might be used to estimate charging current...
\$ I=C \frac{dV}{dt}\$
\$ I = 100\times 10^{-12} \frac {2.7}{2 \times 10^{-6}}\$
\$ I = .135 mA \$...this is within the 0.66mA calculation above.
It is interesting that a discharge spec is not included. It is also interesting that output voltage linearity is not specified between ground and 0.3V. Lack of these specs is consistent with this suggestion that active pull-down current is lacking.

What can you do if a load of 1k is required?
Spec sheet says "don't load with less than 5k".
So you need another external buffer. And you should use one that lightly loads this DAC, and doesn't try to push current back into the pin.