Plot[Evaluate[Eigenvalues[M1]], {t, 0, 10}, PlotLegends -> "Expressions"]

sumofnegativeeigenvalues = Total @ - Ramp @ - Eigenvalues[M1]

-2 Ramp[30 - t] - 

 Ramp[1/2 (-1 - 7 t - Sqrt[1 - 6 t + 9 t^2 + 4 t^4])] - 
 Ramp[1/2 (-1 - 7 t + Sqrt[1 - 6 t + 9 t^2 + 4 t^4])]

Plot[sumofnegativeeigenvalues, {t, 0, 10}, AxesOrigin -> {0, 0}]

Plot[Evaluate[Eigenvalues[M1]], {t, 0, 10}, PlotLegends -> "Expressions"]

sumofnegativeeigenvalues = Total @ - Ramp @ - Eigenvalues[M1]

-2 Ramp[30 - t] - 

 Ramp[1/2 (-1 - 7 t - Sqrt[1 - 6 t + 9 t^2 + 4 t^4])] - 
 Ramp[1/2 (-1 - 7 t + Sqrt[1 - 6 t + 9 t^2 + 4 t^4])]

Plot[sumofnegativeeigenvalues, {t, 0, 10}, AxesOrigin -> {0, 0}]

Alternatively,

ClearAll[sumNegEigenVals]
sumNegEigenVals = Eigenvalues /* Minus /* Ramp /* Minus /* Total;

sumNegEigenVals @ M1 == sumofnegativeeigenvalues

True