ausrutschen
to slip
To lose your footing on a smooth or slippery surface and fall or start sliding.
Vorsicht, der Boden ist nass, damit du nicht ausrutschst!
Careful, the floor is wet, so you don't slip!

to slip
Loading your saved state.
to slip
To lose your footing on a smooth or slippery surface and fall or start sliding.
Vorsicht, der Boden ist nass, damit du nicht ausrutschst!
Careful, the floor is wet, so you don't slip!

'Ausrutschen' (to slip) is a separable verb; the prefix 'aus-' comes at the end in a main clause. Since it describes movement or a sudden change of state, the perfect tense is formed with the auxiliary verb 'sein' (to be).
Ich bin auf dem nassen Laub ausgerutscht.
I slipped on the wet leaves.
In the literal meaning, the slippery surface is usually indicated with the preposition 'auf' and the dative.
Der Postbote ist auf dem vereisten Gehweg ausgerutscht.
The mail carrier slipped on the icy sidewalk.
When someone accidentally says something wrong, a dative construction is used. The person is in the dative, while the thoughtless statement is the subject of the sentence.
Entschuldigung, diese Bemerkung ist mir nur so ausgerutscht.
Sorry, that remark just slipped out.
to fall / overthrow
'stürzen' and 'ausrutschen' can occur in the same situation. 'ausrutschen' names the cause: the ground is smooth or slippery, and you lose your footing. You may fall, but sometimes you only slide briefly. 'stürzen' describes the fall itself, meaning that someone really falls to the ground. Learners confuse the words because people often slip and then fall. If you want to name the cause, use 'ausrutschen'. If you want to emphasize the fall, use 'stürzen'.

Am Morgen rutschte das Kind auf dem nassen Schulhof aus.
In the morning, the child slipped on the wet schoolyard.
Nach dem Gespräch stürzt er auf dem Weg zum Bus und braucht Hilfe.
After the conversation, he falls on the way to the bus and needs help.